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Template:Sequence/list/names/A000000..A000999
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The following documentation is located at Template:Sequence/list/names/A000000..A000999/doc. [<Edit> Template:Sequence/list/names/A000000..A000999/doc]
[⧼Purge⧽ Template:Sequence/list/names/A000000..A000999]
[⧼Purge⧽ Template:Sequence/list/names/A000000..A000999]
The {{sequence/list/names/A000000..A000999}} ({{seq/list/names/A000000..A000999}}) database table template contains a "database" table (of A-numbers A000000 to A000999 and their respective sequence names) that is meant to be used by the {{sequence/list/names}} ({{seq/list/names}}) database template (which is used by the {{sequence}} OEIS Wiki user interface template to show a tooltip with the sequence name).
Warning: In the sequence name, a vertical pipe cannot be used (you must use the the | numeric entity), e.g. for absolute value, otherwise the name gets truncated in the name string produced by this template and/or in the tooltip produced by the {{sequence}} template. (See A000099 in the {{sequence}} template page.)
Contents
Usage
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Examples
Examples with valid input
Code Result {{seq/list/names/A000000..A000999|A0}} The empty sequence. (Although not in the Main OEIS, since it is NOT searchable!) {{seq/list/names/A000000..A000999|A1}} Number of groups of order n. {{seq/list/names/A000000..A000999|A01}} Number of groups of order n. {{seq/list/names/A000000..A000999|A2}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. {{seq/list/names/A000000..A000999|A002}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. {{seq/list/names/A000000..A000999|A3}} Number of classes of primitive binary forms of discriminant D = -4n; or equivalently class number of quadratic order of discriminant D = -4n. {{seq/list/names/A000000..A000999|A37}} Numbers that are not squares. {{seq/list/names/A000000..A000999|A037}} Numbers that are not squares.
Code Result Comment {{seq/list/names/A000000..A000999|A000000}} The empty sequence. (Although not in the Main OEIS, since it is NOT searchable!) {{seq/list/names/A000000..A000999|A000001}} Number of groups of order n. {{seq/list/names/A000000..A000999|A000002}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. {{seq/list/names/A000000..A000999|A000003}} Number of classes of primitive binary forms of discriminant D = -4n; or equivalently class number of quadratic order of discriminant D = -4n. {{seq/list/names/A000000..A000999|A000004}} The zero sequence. {{seq/list/names/A000000..A000999|A000095}} Number of fixed points of GAMMA_0 (n) of type i. {{seq/list/names/A000000..A000999|A000096}} n*(n+3)/2. {{seq/list/names/A000000..A000999|A000097}} Number of partitions of n if there are two kinds of 1's and two kinds of 2's. {{seq/list/names/A000000..A000999|A000098}} Number of partitions of n if there are two kinds of 1, two kinds of 2 and two kinds of 3. {{seq/list/names/A000000..A000999|A000099}} Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record. (The vertical pipe must be replaced by the | numeric entity.)
Code Result {{seq/list/names/A000000..A000999|A000100}} a(n) = number of compositions of n in which the maximum part size is 3. {{seq/list/names/A000000..A000999|A000101}} Increasing gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps). {{seq/list/names/A000000..A000999|A000102}} a(n) = number of compositions of n in which the maximum part size is 4. {{seq/list/names/A000000..A000999|A000103}} Number of n-node triangulations of sphere in which every node has degree >= 4. {{seq/list/names/A000000..A000999|A000104}} Number of n-celled polyominoes without holes. {{seq/list/names/A000000..A000999|A000195}} log(n) rounded down. {{seq/list/names/A000000..A000999|A000196}} Integer part of square root of n. Or, number of squares <= n. Or, n appears 2n+1 times. {{seq/list/names/A000000..A000999|A000197}} (n!)!. {{seq/list/names/A000000..A000999|A000198}} Largest order of automorphism group of a tournament with n nodes. {{seq/list/names/A000000..A000999|A000199}} Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).
Code Result {{seq/list/names/A000000..A000999|A000200}} Number of bicentered hydrocarbons with n atoms. {{seq/list/names/A000000..A000999|A000201}} Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2. {{seq/list/names/A000000..A000999|A000202}} a(8i+j) = 13i + a(j), where 1<=j<=8. {{seq/list/names/A000000..A000999|A000203}} sigma(n) = sum of divisors of n. Also called sigma_1(n). {{seq/list/names/A000000..A000999|A000204}} Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3. {{seq/list/names/A000000..A000999|A000295}} Eulerian numbers (Euler's triangle: column k=2 of A008292, column k=1 of A173018) {{seq/list/names/A000000..A000999|A000296}} Number of partitions of an n-set into blocks of size >1. Also number of cyclically spaced (or feasible) partitions. {{seq/list/names/A000000..A000999|A000297}} (n+1)*(n+3)*(n+8)/6. {{seq/list/names/A000000..A000999|A000298}} Number of partitions into non-integral powers. {{seq/list/names/A000000..A000999|A000299}} Number of n-node rooted trees of height 4.
Code Result {{seq/list/names/A000000..A000999|A000300}} 4th power of rooted tree enumerator: linear forests of 4 rooted trees. {{seq/list/names/A000000..A000999|A000301}} a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=2; also a(n) = 2^Fibonacci(n). {{seq/list/names/A000000..A000999|A000302}} Powers of 4. {{seq/list/names/A000000..A000999|A000303}} Number of permutations of [n] in which the longest increasing run has length 2. {{seq/list/names/A000000..A000999|A000304}} a(n) = a(n-1) a(n-2). {{seq/list/names/A000000..A000999|A000395}} 6th power of rooted tree enumerator; number of linear forests of 6 rooted trees. {{seq/list/names/A000000..A000999|A000396}} Perfect numbers n: n is equal to the sum of the proper divisors of n. {{seq/list/names/A000000..A000999|A000397}} Number of partitions into non-integral powers. {{seq/list/names/A000000..A000999|A000398}} Numbers of form x^2 + 2y^2 + 2yz + 4z^2. {{seq/list/names/A000000..A000999|A000399}} Unsigned Stirling numbers of first kind s(n,3).
Code Result {{seq/list/names/A000000..A000999|A000400}} Powers of 6. {{seq/list/names/A000000..A000999|A000401}} Numbers of form x^2 + y^2 + 2z^2. {{seq/list/names/A000000..A000999|A000402}} Number of permutations of [n] in which the longest increasing run has length 3. {{seq/list/names/A000000..A000999|A000403}} Number of simple equifacetted 3-manifolds with n faces. {{seq/list/names/A000000..A000999|A000404}} Numbers that are the sum of 2 nonzero squares. {{seq/list/names/A000000..A000999|A000495}} Nearest integer to sinh(n). {{seq/list/names/A000000..A000999|A000496}} Restricted permutations. {{seq/list/names/A000000..A000999|A000497}} S2(j,2j+2) where S2(n,k) is a 2-associated Stirling number of the second kind. {{seq/list/names/A000000..A000999|A000498}} Eulerian numbers (Euler's triangle: column k=4 of A008292, column k=3 of A173018) {{seq/list/names/A000000..A000999|A000499}} Related to the divisor function.
Code Result {{seq/list/names/A000000..A000999|A000500}} Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-7 places. {{seq/list/names/A000000..A000999|A000501}} Floor( cosh(n) ). {{seq/list/names/A000000..A000999|A000502}} Number of genus 0 rooted maps with 6 faces with n vertices {{seq/list/names/A000000..A000999|A000503}} Floor(tan(n)). {{seq/list/names/A000000..A000999|A000504}} S2(j,2j+3) where S2(n,k) is a 2-associated Stirling number of the second kind. {{seq/list/names/A000000..A000999|A000595}} Number of nonisomorphic unlabeled binary relations on n nodes. {{seq/list/names/A000000..A000999|A000596}} Central factorial numbers. {{seq/list/names/A000000..A000999|A000597}} Central factorial numbers. {{seq/list/names/A000000..A000999|A000598}} Number of rooted ternary trees with n nodes; number of n-carbon alkyl radicals C(n)H(2n+1) ignoring stereoisomers. {{seq/list/names/A000000..A000999|A000599}} Number of secondary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms.
Code Result {{seq/list/names/A000000..A000999|A000600}} Number of tertiary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms. {{seq/list/names/A000000..A000999|A000601}} Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)). {{seq/list/names/A000000..A000999|A000602}} Number of n-node unrooted quartic trees; number of n-carbon alkanes C(n)H(2n+2) ignoring stereoisomers. {{seq/list/names/A000000..A000999|A000603}} Number of nonnegative solutions to x^2 + y^2 <= n^2. {{seq/list/names/A000000..A000999|A000604}} Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2. {{seq/list/names/A000000..A000999|A000695}} Moser-de Bruijn sequence: sums of distinct powers of 4. {{seq/list/names/A000000..A000999|A000696}} Numbers n such that (1,n) is "good". {{seq/list/names/A000000..A000999|A000697}} Boustrophedon transform of squares 1,1,4,9,16,... {{seq/list/names/A000000..A000999|A000698}} A problem of configurations: a(0) = 1; for n>0, a(n) = (2n-1)!! - Sum_{k=1..n-1} (2k-1)!! a(n-k). Also the number of shellings of an n-cube, divided by 2^n n!. {{seq/list/names/A000000..A000999|A000699}} Number of irreducible diagrams with 2n nodes.
Code Result {{seq/list/names/A000000..A000999|A000700}} Expansion of product (1+x^(2k+1)), k=0..inf; number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes. {{seq/list/names/A000000..A000999|A000701}} One half of number of non-self-conjugate partitions; also half of number of asymmetric Ferrers graphs with n nodes. {{seq/list/names/A000000..A000999|A000702}} a(n) = number of conjugacy classes in the alternating group A_n. {{seq/list/names/A000000..A000999|A000703}} Chromatic number (or Heawood number) of nonorientable surface with n crosscaps. {{seq/list/names/A000000..A000999|A000704}} Number of degree-n even permutations of order dividing 2. {{seq/list/names/A000000..A000999|A000795}} Salie numbers: expansion of cosh x / cos x = Sum_{n >= 0} a(n)*x^(2n)/(2n)!. {{seq/list/names/A000000..A000999|A000796}} Decimal expansion of Pi. {{seq/list/names/A000000..A000999|A000797}} Numbers that are not the sum of 4 tetrahedral numbers. {{seq/list/names/A000000..A000999|A000798}} Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements. {{seq/list/names/A000000..A000999|A000799}} Floor( 2^n /n ).
Code Result {{seq/list/names/A000000..A000999|A000800}} Sum of upward diagonals of Eulerian triangle. {{seq/list/names/A000000..A000999|A000801}} Sum_{k = 1..n} floor(2^k / k). {{seq/list/names/A000000..A000999|A000802}} Maximal number of states in deterministic finite automaton accepting a language consisting of some words of length n. {{seq/list/names/A000000..A000999|A000803}} a(n+3)=a(n+2)+a(n+1)+a(n)-4. {{seq/list/names/A000000..A000999|A000804}} Permanent of a certain cyclic n X n (0,1) matrix. {{seq/list/names/A000000..A000999|A000895}} Number of switching networks with AG(n,2) acting on the domain and AG(2,2) acting on the range. {{seq/list/names/A000000..A000999|A000896}} Number of switching networks with AG(n,2) acting on the domain and AG(3,2) acting on the range. {{seq/list/names/A000000..A000999|A000897}} (4n)! / ((2n)! n!^2). {{seq/list/names/A000000..A000999|A000898}} a(n) = 2(a(n-1) + (n-1)a(n-2)). {{seq/list/names/A000000..A000999|A000899}} Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
Code Result {{seq/list/names/A000000..A000999|A000900}} Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details). {{seq/list/names/A000000..A000999|A000901}} Number of solutions to the rook problem on a 2n X 2n board having a certain symmetry group (see Robinson for details). {{seq/list/names/A000000..A000999|A000902}} E.g.f.: (1/2)*(exp(2x + x^2) + 1). {{seq/list/names/A000000..A000999|A000903}} Number of inequivalent ways of placing n nonattacking rooks on n X n board. {{seq/list/names/A000000..A000999|A000904}} a(n) = (n + 1) a(n - 1) + (n + 2) a(n - 2) + a(n - 3); a(1)=0, a(2)=3, a(3)=13. {{seq/list/names/A000000..A000999|A000995}} Shifts left two terms under the binomial transform. {{seq/list/names/A000000..A000999|A000996}} Shifts 3 places left under binomial transform. {{seq/list/names/A000000..A000999|A000997}} From a differential equation. {{seq/list/names/A000000..A000999|A000998}} From a differential equation. {{seq/list/names/A000000..A000999|A000999}} 5^a(n) divides C(2n,n).
Examples with out-of-range input
Code Result {{seq/list/names/A000000..A000999|A001000}} A001000 {{seq/list/names/A000000..A000999|A100000}} A100000 {{seq/list/names/A000000..A000999|A100001}} A100001 {{seq/list/names/A000000..A000999|A200000}} A200000 {{seq/list/names/A000000..A000999|A200001}} A200001
Examples with invalid input
Validation is done by the {{sequence/list/names}} ({{seq/list/names}}) template.
Contents of sequence names database table (A000000..A000999)
Autopopulating the sequence names database tables via a script
See Template:Sequence/list/names/doc#Autopopulating the sequence names database tables via a script.
Format of sequence names database tables
See Template:Sequence/list/names/doc#Format of sequence names database tables.
Extracted (A000001 to A000999) from the following OEIS file:
# OEIS Sequence Names (http://oeis.org/names.gz) # Last Modified: February 15 03:34 EST 2013 # Use of this content is governed by the # OEIS End-User License: http://oeis.org/LICENSE
A000000 as stand-in for: The empty sequence. (Although not in the Main OEIS, since it is NOT searchable!)
Only A000001 to A000999 have been extracted here!
BUG ALERT: vertical pipes in names (e.g. for absolute value) will cause havoc! We will have to use the {{!}} work-around template!
Sequence names database table (A000000 to A000999)
| A000001 = Number of groups of order n. | A000002 = Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. | A000003 = Number of classes of primitive binary forms of discriminant D = -4n; or equivalently class number of quadratic order of discriminant D = -4n. | A000004 = The zero sequence. | A000005 = d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n. | A000006 = Integer part of square root of n-th prime. | A000007 = The characteristic function of 0: a(n) = 0^n. | A000008 = Number of ways of making change for n cents using coins of 1, 2, 5, 10 cents. | A000009 = Expansion of Product_{m=1..infinity} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts. | A000010 = Euler totient function phi(n): count numbers <= n and prime to n. | A000011 = Number of n-bead necklaces (turning over is allowed) where complements are equivalent. | A000012 = The simplest sequence of positive numbers: the all 1's sequence. | A000013 = Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed. | A000014 = Number of series-reduced trees with n nodes. | A000015 = Smallest prime power >= n. | A000016 = a(n) = number of distinct (infinite) output sequences from binary n-stage shift register which feeds back the complement of the last stage. E.g. for n=6 there are 6 such sequences. | A000017 = Erroneous version of A032522. | A000018 = Number of positive integers <= 2^n of form x^2 + 16y^2. | A000019 = Number of primitive permutation groups of degree n. | A000020 = Number of primitive polynomials of degree n over GF(2). | A000021 = Number of positive integers <= 2^n of form x^2 + 12 y^2. | A000022 = Number of centered hydrocarbons with n atoms. | A000023 = E.g.f.: exp(-2*x)/(1-x). | A000024 = Number of positive integers <= 2^n of form x^2 + 10 y^2. | A000025 = Coefficients of the 3rd order mock theta function f(q) | A000026 = Mosaic numbers or multiplicative projection of n. | A000027 = The natural numbers. Also called the whole numbers, the counting numbers or the positive integers. | A000028 = Let n = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives n such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd. | A000029 = Number of necklaces with n beads of 2 colors, allowing turning over. | A000030 = Initial digit of n. | A000031 = Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n. | A000032 = Lucas numbers (beginning at 2): L(n) = L(n-1) + L(n-2). (Cf. A000204.) | A000033 = Coefficients of menage hit polynomials. | A000034 = Period 2: repeat (1,2); a(n) = 1+n mod 2. | A000035 = Period 2: (0, 1) repeated; a(n) = n mod 2. | A000036 = Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); A000099 gives values of n where |P(n)| sets a new record; sequence gives closest integer to P(A000099(n)). | A000037 = Numbers that are not squares. | A000038 = Twice A000007. | A000039 = Coefficient of q^(2n) in the series expansion of Ramanujan's mock theta function f(q). | A000040 = The prime numbers. | A000041 = a(n) = number of partitions of n (the partition numbers). | A000042 = Unary representation of natural numbers. | A000043 = Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime. | A000044 = Dying rabbits: a(0) = 1; for 1 <= n <= 12, a(n) = Fibonacci(n); for n >= 13, a(n) = a(n-1)+a(n-2)-a(n-13). | A000045 = Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1. | A000046 = Number of primitive n-bead necklaces (turning over is allowed) where complements are equivalent. | A000047 = Number of integers <= 2^n of form x^2 - 2y^2. | A000048 = Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged. | A000049 = Number of positive integers <= 2^n of form 3 x^2 + 4 y^2. | A000050 = Number of positive integers <= 2^n of form x^2 + y^2. | A000051 = 2^n + 1. | A000052 = 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc. | A000053 = Local stops on New York City Broadway line (IRT #1) subway. | A000054 = Local stops on New York City A line subway. | A000055 = Number of trees with n unlabeled nodes. | A000056 = Order of the group SL(2,Z_n). | A000057 = Primes dividing all Fibonacci sequences. | A000058 = Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(0) = 2. | A000059 = Numbers n such that (2n)^4 + 1 is prime. | A000060 = Number of signed trees with n nodes. | A000061 = Generalized tangent numbers d(n,1). | A000062 = A Beatty sequence: [ n/(e-2) ]. | A000063 = Symmetrical dissections of an n-gon. | A000064 = Partial sums of (unordered) ways of making change for n cents using coins of 1, 2, 5, 10 cents. | A000065 = -1 + number of partitions of n. | A000066 = Smallest number of vertices in trivalent graph with girth (shortest cycle) = n. | A000067 = Number of positive integers <= 2^n of form x^2 + 2 y^2. | A000068 = Numbers n such that n^4 + 1 is prime. | A000069 = Odious numbers: numbers with an odd number of 1's in their binary expansion. | A000070 = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041). | A000071 = Fibonacci numbers - 1. | A000072 = Number of positive integers <= 2^n of form x^2 + 4 y^2. | A000073 = Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=0, a(2)=1. | A000074 = Number of odd integers <= 2^n of form x^2 + y^2. | A000075 = Number of positive integers <= 2^n of form 2 x^2 + 3 y^2. | A000076 = Number of integers <= 2^n of form 4 x^2 + 4 x y + 5 y^2. | A000077 = Number of positive integers <= 2^n of form x^2 + 6 y^2 | A000078 = Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) with a(0)=a(1)=a(2)=0, a(3)=1. | A000079 = Powers of 2: a(n) = 2^n. | A000080 = Number of nonisomorphic minimal triangle graphs. | A000081 = Number of rooted trees with n nodes (or connected functions with a fixed point). | A000082 = n^2*Product_{p|n} (1 + 1/p). | A000083 = Number of mixed Husimi trees with n nodes; or polygonal cacti with bridges. | A000084 = Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon. | A000085 = Number of self-inverse permutations on n letters, also known as involutions; number of Young tableaux with n cells. | A000086 = Number of solutions to x^2 - x + 1 == 0 (mod n). | A000087 = Number of rooted planar maps. | A000088 = Number of graphs on n unlabeled nodes. | A000089 = Number of solutions to x^2 + 1 == 0 (mod n). | A000090 = E.g.f. exp((-x^3)/3)/(1-x). | A000091 = Multiplicative with a(2^k) = 2 for k >= 1; a(3) = 2, a(3^k) = 0 for k >= 2; a(p) = 0 if p >3 and p == -1 mod 3; a(p) = 2 if p > 3 and p == 1 mod 3. | A000092 = Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record. | A000093 = floor(n^(3/2)). | A000094 = Number of trees of diameter 4. | A000095 = Number of fixed points of GAMMA_0 (n) of type i. | A000096 = n*(n+3)/2. | A000097 = Number of partitions of n if there are two kinds of 1's and two kinds of 2's. | A000098 = Number of partitions of n if there are two kinds of 1, two kinds of 2 and two kinds of 3. | A000099 = Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record. | A000100 = a(n) = number of compositions of n in which the maximum part size is 3. | A000101 = Increasing gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps). | A000102 = a(n) = number of compositions of n in which the maximum part size is 4. | A000103 = Number of n-node triangulations of sphere in which every node has degree >= 4. | A000104 = Number of n-celled polyominoes without holes. | A000105 = Number of free polyominoes (or square animals) with n cells. | A000106 = 2nd power of rooted tree enumerator; number of linear forests of 2 rooted trees. | A000107 = Number of rooted trees with n nodes and a single labeled node; pointed rooted trees; vertebrates. | A000108 = Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!). Also called Segner numbers. | A000109 = Number of simplicial polyhedra with n nodes; simple planar graphs with 3n-6 edges; maximal simple planar graphs; 3-connected planar triangulations; 3-connected triangulations of the sphere; 3-connected cubic planar graphs. | A000110 = Bell or exponential numbers: ways of placing n labeled balls into n indistinguishable boxes. | A000111 = Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also number of alternating permutations on n letters. | A000112 = Number of partially ordered sets ("posets") with n unlabeled elements. | A000113 = Number of transformation groups of order n. | A000114 = Number of cusps of principal congruence subgroup GAMMA^{hat}(n). | A000115 = Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)). | A000116 = Number of even sequences with period 2n (bisection of A000013). | A000117 = Number of even sequences with period 2n (bisection of A000011). | A000118 = Number of ways of writing n as a sum of 4 squares; theta series of lattice Z^4. | A000119 = Number of representations of n as a sum of distinct Fibonacci numbers. | A000120 = 1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n). | A000121 = Number of representations of n as a sum of Fibonacci numbers (1 is allowed twice as a part). | A000122 = Expansion of Jacobi theta function theta_3(x) = Sum_{m = -infinity..infinity} x^(m^2) (number of solutions to k^2 = n). | A000123 = Number of binary partitions: number of partitions of 2n into powers of 2. | A000124 = Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts. | A000125 = Cake numbers: maximal number of pieces resulting from n planar cuts through a cube (or cake): C(n+1,3)+n+1. | A000126 = A nonlinear binomial sum. | A000127 = Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes. | A000128 = A nonlinear binomial sum. | A000129 = Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2). | A000130 = One-half the number of permutations of length n with exactly 1 rising or falling successions. | A000131 = Number of asymmetrical dissections of n-gon. | A000132 = Number of ways of writing n as a sum of 5 squares. | A000133 = Number of Boolean functions of n variables. | A000134 = Positive zeros of Bessel function of order 0 rounded to nearest integer. | A000135 = Number of partitions into non-integral powers. | A000136 = Number of ways of folding a strip of n labeled stamps. | A000137 = Series-parallel numbers. | A000138 = E.g.f. exp(-x^4/4)/(1-x). | A000139 = a(n) = 2*(3*n)!/((2*n+1)!*((n+1)!)). | A000140 = Kendall-Mann numbers: the maximal number of inversions in a permutation on n letters is floor(n(n-1)/4); a(n) = number of permutations with this many inversions. | A000141 = Number of ways of writing n as a sum of 6 squares. | A000142 = Factorial numbers: n! = 1*2*3*4*...*n (order of symmetric group S_n, number of permutations of n letters). | A000143 = Number of ways of writing n as a sum of 8 squares. | A000144 = Number of ways of writing n as a sum of 10 squares. | A000145 = Number of ways of writing n as a sum of 12 squares. | A000146 = From von Staudt-Clausen representation of Bernoulli numbers: a(n) = Bernoulli(2n) + Sum_{(p-1)|2n} 1/p. | A000147 = Number of trees of diameter 5. | A000148 = Number of partitions into non-integral powers. | A000149 = Floor(e^n). | A000150 = Number of dissections of an n-gon, rooted at an exterior edge, asymmetric with respect to that edge. | A000151 = Number of oriented rooted trees with n nodes. Also rooted trees with n nodes and 2-colored non-root nodes. | A000152 = Number of ways of writing n as a sum of 16 squares. | A000153 = a(n) = n*a(n-1) + (n-2)*a(n-2), with a(0) = 0, a(1) = 1. | A000154 = Erroneous version of A003713. | A000155 = Nearest integer to modified Bessel function K_n(1). | A000156 = Number of ways of writing n as a sum of 24 squares. | A000157 = Number of Boolean functions of n variables. | A000158 = Number of partitions into non-integral powers. | A000159 = Coefficients of menage hit polynomials. | A000160 = Number of partitions into non-integral powers. | A000161 = Number of partitions of n into 2 squares. | A000162 = Number of 3-dimensional polyominoes (or polycubes) with n cells. | A000163 = Series-parallel numbers. | A000164 = Number of partitions of n into 3 squares. | A000165 = Double factorial of even numbers: (2n)!! = 2^n*n!. | A000166 = Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points. | A000167 = Nearest integer to modified Bessel function K_n(2). | A000168 = 2*3^n*(2*n)!/(n!*(n+2)!). | A000169 = Number of labeled rooted trees with n nodes: n^(n-1). | A000170 = Number of ways of placing n nonattacking queens on n X n board. | A000171 = Number of self-complementary graphs with n nodes. | A000172 = Franel number a(n) = Sum C(n,k)^3, k=0..n. | A000173 = Unitary-sociable numbers (smallest member of each cycle). | A000174 = Number of partitions of n into 5 squares. | A000175 = Related to zeros of Bessel function. | A000176 = Generalized tangent numbers d_(n,2). | A000177 = Number of partitions of n into 6 squares. | A000178 = Superfactorials: product of first n factorials. | A000179 = Menage numbers: number of permutations s of [0, ..., n-1] such that s(i) != i and s(i) != i+1 (mod n) for all i. | A000180 = Expansion of e^(-x)/(1-3x). | A000181 = Coefficients of menage hit polynomials. | A000182 = Tangent (or "Zag") numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x). | A000183 = Number of discordant permutations of length n. | A000184 = Number of genus 0 rooted maps with 3 faces with n vertices. | A000185 = Coefficients of menage hit polynomials. | A000186 = Number of 3 X n Latin rectangles in which the first row is in order. | A000187 = Generalized Euler numbers, c(5,n). | A000188 = (1) Number of solutions to x^2 = 0 (mod n). (2) Also square root of largest square dividing n. (3) Also Max_{ d divides n } GCD[d,n/d]. | A000189 = Number of solutions to x^3 == 0 (mod n). | A000190 = Number of solutions to x^4 == 0 (mod n). | A000191 = Generalized tangent numbers d(3,n). | A000192 = Generalized Euler numbers c(6,n). | A000193 = Nearest integer to log n. | A000194 = n appears 2n times; also nearest integer to square root of n. | A000195 = log(n) rounded down. | A000196 = Integer part of square root of n. Or, number of squares <= n. Or, n appears 2n+1 times. | A000197 = (n!)!. | A000198 = Largest order of automorphism group of a tournament with n nodes. | A000199 = Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).
| A000200 = Number of bicentered hydrocarbons with n atoms. | A000201 = Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2. | A000202 = a(8i+j) = 13i + a(j), where 1<=j<=8. | A000203 = sigma(n) = sum of divisors of n. Also called sigma_1(n). | A000204 = Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3. | A000205 = Number of positive integers <= 2^n of form x^2 + 3 y^2. | A000206 = Even sequences with period 2n. | A000207 = Number of inequivalent ways of dissecting a regular (n+2)-gon into n triangles by n-1 non-intersecting diagonals under rotations and reflections; also the number of planar 2-trees. | A000208 = Number of even sequences with period 2n. | A000209 = Nearest integer to tan n. | A000210 = A Beatty sequence: [ n (e-1) ]. | A000211 = a(n) = a(n-1) + a(n-2) - 2. | A000212 = Floor(n^2/3). | A000213 = Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=a(2)=1. | A000214 = Number of equivalence classes of Boolean functions of n variables under action of AG(n,2). | A000215 = Fermat numbers: 2^(2^n) + 1, n >= 0. | A000216 = Take sum of squares of digits of previous term. | A000217 = Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n. | A000218 = Take sum of squares of digits of previous term. | A000219 = Number of planar partitions of n. | A000220 = Number of asymmetric trees with n nodes (also called identity trees). | A000221 = Take sum of squares of digits of previous term. | A000222 = Coefficients of menage hit polynomials. | A000223 = Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A00092(n)). | A000224 = Number of squares mod n. | A000225 = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.) | A000226 = Number of n-node unlabeled connected graphs with one cycle of length 3. | A000227 = Nearest integer to e^n. | A000228 = Number of hexagonal polyominoes (or planar polyhexes) with n cells. | A000229 = a(n) is the least number such that the n-th prime is the least quadratic nonresidue for a(n) (a(n) is always a prime). | A000230 = Smallest prime p such that there is a gap of 2n between p and next prime. | A000231 = Number of inequivalent Boolean functions of n variables under action of complementing group. | A000232 = Construct a triangle as in A036262. Sequence is one less than the position of the first number larger than 2 in the n-th row (n-th difference). | A000233 = Generalized class numbers. | A000234 = Partitions into non-integral powers (see Comments for precise definition). | A000235 = Number of n-node rooted trees of height 3. | A000236 = Maximum m such that there are no two adjacent elements belonging to the same n-th power residue class modulo some prime p in the sequence 1,2,...,m (equivalently, there is no n-th power residue modulo p in the sequence 1/2,2/3,...,(m-1)/m). | A000237 = Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges. | A000238 = Number of oriented trees with n nodes. | A000239 = Number of permutations of length n by rises. | A000240 = Rencontres numbers: permutations with exactly one fixed point. | A000241 = Crossing number of complete graph with n nodes. Dubious for n >= 13. | A000242 = 3rd power of rooted tree enumerator; number of linear forests of 3 rooted trees. | A000243 = Number of trees with n nodes, 2 of which are labeled. | A000244 = Powers of 3. | A000245 = 3*(2*n)!/((n+2)!*(n-1)!). | A000246 = Number of permutations in the symmetric group S_n that have odd order. | A000247 = 2^n-n-2. | A000248 = Number of forests with n nodes and height at most 1. | A000249 = Nearest integer to modified Bessel function K_n(5). | A000250 = Number of symmetric reflexive relations on n nodes: (1/2)*A000666. | A000251 = Number of trees of diameter 6. | A000252 = Number of invertible 2 X 2 matrices mod n. | A000253 = a(n) = 2a(n-1)-a(n-2)+a(n-3)+2^(n-1). | A000254 = Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1)=(n+1)*a(n)+n!. | A000255 = a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1. | A000256 = Number of simple triangulations of plane with n nodes. | A000257 = Number of rooted bicubic maps: a(n)=(8n-4)a(n-1)/(n+2). | A000258 = E.g.f.: exp(exp(exp(x)-1)-1). | A000259 = Number of certain rooted planar maps. | A000260 = Number of rooted simplicial 3-polytopes with n+3 nodes; or rooted 3-connected triangulations with 2n+2 faces; or rooted 3-connected trivalent maps with 2n+2 vertices. | A000261 = a(n) = n*a(n-1) + (n-3)*a(n-2). | A000262 = Number of "sets of lists": number of partitions of {1,...,n} into any number of lists, where a list means an ordered subset. | A000263 = Number of partitions into non-integral powers. | A000264 = Number of 3-edge-connected rooted cubic maps with 2n nodes and a distinguished Hamilton cycle | A000265 = Remove 2's from n; or largest odd divisor of n; or odd part of n. | A000266 = Expansion of exp (-x^2 /2) / (1-x). | A000267 = Integer part of square root of 4n+1. | A000268 = E.g.f.: -ln(1+ln(1+ln(1-x))). | A000269 = Number of trees with n nodes, 3 of which are labeled. | A000270 = Number of discordant permutations. | A000271 = Sums of menage numbers. | A000272 = Number of trees on n labeled nodes: n^(n-2) with a(0)=1. | A000273 = Number of directed graphs (or digraphs) with n nodes. | A000274 = Number of permutations of length n by rises. | A000275 = Coefficients of a Bessel function (reciprocal of J_0(z)); also pairs of permutations with rise/rise forbidden. | A000276 = Associated Stirling numbers. | A000277 = 3*n - 2*floor(sqrt(4*n+5)) + 5. | A000278 = a(n) = a(n-1) + a(n-2)^2. | A000279 = Card matching. | A000280 = a(n) = a(n-1) + a(n-2)^3. | A000281 = Expansion of cos(x)/cos(2x). | A000282 = Finite automata. | A000283 = a(n) = a(n-1)^2 + a(n-2)^2. | A000284 = a(n) = a(n-1)^3 + a(n-2). | A000285 = a(0) = 1, a(1) = 4, and a(n) = a(n-1) + a(n-2) for n>=2. | A000286 = Number of positive integers <= 2^n of form 2 x^2 + 5 y^2. | A000287 = Number of rooted polyhedral graphs with n edges. | A000288 = Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) with a(0)=a(1)=a(2)=a(3)=1. | A000289 = A nonlinear recurrence: a(n) = a(n-1)^2-3*a(n-1)+3 (for n>1). | A000290 = The squares: a(n) = n^2. | A000291 = Number of bipartite partitions of n white objects and 2 black ones. | A000292 = Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6. | A000293 = a(n) = number of solid (i.e. three-dimensional) partitions of n. | A000294 = G.f.: Product_{k >= 1} (1 - x^k)^(-k*(k+1)/2). | A000295 = Eulerian numbers (Euler's triangle: column k=2 of A008292, column k=1 of A173018) | A000296 = Number of partitions of an n-set into blocks of size >1. Also number of cyclically spaced (or feasible) partitions. | A000297 = (n+1)*(n+3)*(n+8)/6. | A000298 = Number of partitions into non-integral powers. | A000299 = Number of n-node rooted trees of height 4.
| A000300 = 4th power of rooted tree enumerator: linear forests of 4 rooted trees. | A000301 = a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=2; also a(n) = 2^Fibonacci(n). | A000302 = Powers of 4. | A000303 = Number of permutations of [n] in which the longest increasing run has length 2. | A000304 = a(n) = a(n-1) a(n-2). | A000305 = Number of certain rooted planar maps. | A000306 = Number of trees of diameter 8. | A000307 = Number of 4-level labeled rooted trees with n leaves. | A000308 = a(n)=a(n-1)*a(n-2)*a(n-3) with a(1)=1, a(2)=2 and a(3)=3. | A000309 = Number of rooted cubic maps with 2n nodes. | A000310 = Coefficients of iterated exponentials. | A000311 = Schroeder's fourth problem; also number of phylogenetic trees with n nodes; also number of total partitions of n. | A000312 = Number of labeled mappings from n points to themselves (endofunctions): n^n. | A000313 = Number of permutations of length n by rises. | A000314 = Number of mixed Husimi trees with n nodes; or labeled polygonal cacti with bridges. | A000315 = Number of reduced Latin squares of order n; labeled loops (quasigroups with an identity element) and a fixed identity. | A000316 = Number of permutations with no hits on 2 main diagonals. | A000317 = a(n+1) = a(n)^2 - a(n) a(n-1) + a(n-1)^2. | A000318 = Generalized tangent numbers d(4,n). | A000319 = a(n) = floor(b(n)), where b(n)=tan(b(n-1)), b(0)=1. | A000320 = Generalized tangent numbers d(5,n). | A000321 = H_n(-1/2), where H_n(x) is Hermite polynomial of degree n. | A000322 = Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) with a(0)=a(1)=a(2)=a(3)=a(4)=1. | A000323 = Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); A000099 gives values of n where |P(n)| sets a new record; sequence gives A(A000099(n)). | A000324 = A nonlinear recurrence: a(n) = a(n-1)^2 - 4*a(n-1) + 4 (for n>1). | A000325 = 2^n - n. | A000326 = Pentagonal numbers: n*(3*n-1)/2. | A000327 = Number of partitions into non-integral powers. | A000328 = Number of points of norm <= n^2 in square lattice. | A000329 = Nearest integer to b(n), where b(n)=tan(b(n-1)), b(0)=1. | A000330 = Square pyramidal numbers: 0^2 + 1^2 + 2^2 +...+ n^2 = n*(n+1)*(2*n+1)/6. | A000331 = Related to zeros of Bessel function. | A000332 = Binomial coefficients binomial(n,4). | A000333 = Number of partitions into non-integral powers. | A000334 = Number of 4-dimensional partitions of n. | A000335 = Euler transform of A000292. | A000336 = a(n) = a(n-1) a(n-2) a(n-3) a(n-4). | A000337 = (n-1)*2^n + 1. | A000338 = Expansion of (5-2x)(1-x^3)/(1-x)^4. | A000339 = Number of partitions into non-integral powers. | A000340 = a(0)=1, a(n)=3*a(n-1)+n+1. | A000341 = Number of ways to pair up {1..2n} so sum of each pair is prime. | A000342 = Number of n-node rooted trees of height 5. | A000343 = 5th power of rooted tree enumerator; number of linear forests of 5 rooted trees. | A000344 = 5*binomial(2n,n-2)/(n+3). | A000345 = Number of partitions into non-integral powers. | A000346 = 2^(2*n+1) - binomial(2*n+1,n+1). | A000347 = Number of partitions into non-integral powers. | A000348 = Number of ways to pair up {1^2, 2^2, ..., (2n)^2 } so sum of each pair is prime. | A000349 = One-half the number of permutations of length n with exactly 2 rising or falling successions. | A000350 = Numbers n such that Fibonacci(n) ends with n. | A000351 = Powers of 5. | A000352 = One half of the number of permutations of [n] such that the differences have three runs with the same signs. | A000353 = Primes == 7, 19, 23 (mod 40) such that (p-1)/2 is also prime. | A000354 = E.g.f. exp(-x)/(1-2*x). | A000355 = Primes = 3, 9, 11 (mod 20) such that 2p+1 is also prime. | A000356 = Number of rooted cubic maps with 2n nodes and a distinguished Hamilton cycle: (2n)!(2n+1)!/(n!^2*(n+1)!(n+2)!). | A000357 = Number of 5-level labeled rooted trees with n leaves. | A000358 = Number of binary necklaces of length n with no subsequence 00. | A000359 = Coefficients of iterated exponentials. | A000360 = From a fat-fractal triangle which happens to be a self-replicating tiling. | A000361 = From a fractal set of positive Lebesgue measure, a self-replicating tiling with holes, the 4-reptile following the 2-reptile of Paul Levy. | A000362 = Generalized class numbers c_(n,2). | A000363 = Number of permutations of [n] with exactly 2 increasing runs of length at least 2. | A000364 = Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sech(x)=1/cosh(x). | A000365 = Number of genus 0 rooted planar maps with n vertices. | A000366 = Genocchi numbers of second kind (A005439) divided by 2^(n-1). | A000367 = Numerators of Bernoulli numbers B_2n. | A000368 = Number of connected graphs with one cycle of length 4. | A000369 = Triangle of numbers related to triangle A049213; generalization of Stirling numbers of second kind A008277, Bessel triangle A001497. | A000370 = NPN-equivalence classes of Boolean functions of n or fewer variables. | A000371 = a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*2^(2^k). | A000372 = Dedekind numbers or Dedekind's problem: number of monotone Boolean functions of n variables, number of antichains of subsets of an n-set, number of elements in a free distributive lattice on n generators, number of Sperner families. | A000373 = Conjectured dimension of a module associated with the free commutative Moufang loop with n generators. | A000374 = Number of cycles (mod n) under doubling map. | A000375 = Topswops (1): start by shuffling n cards labeled 1..n. If top card is m, reverse order of top m cards, then repeat. a(n) is the maximal number of steps before top card is 1. | A000376 = Topswops (2): start by shuffling n cards labeled 1..n. If top card is m, reverse order of top m cards. Repeat until 1 gets to top, then stop. Suppose the whole deck is now sorted (if not, discard this case). a(n) is the maximal number of steps before 1 got to the top. | A000377 = Expansion of f(-q^3) * f(-q^8) * chi(-q^12) / chi(-q) in powers of q where chi(), f() are Ramanujan theta functions. | A000378 = Numbers of the form x^2 + y^2 + z^2 (x, y, z >= 0). | A000379 = A 2-way classification of integers: complement of A000028. | A000380 = Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-3 places. | A000381 = Essentially the same as A001611. | A000382 = Restricted permutations. | A000383 = Hexanacci numbers with a(0)=...=a(5)=1. | A000384 = Hexagonal numbers: n*(2*n-1). | A000385 = Convolution of A000203 with itself. | A000386 = Coefficients of menage hit polynomials. | A000387 = Rencontres numbers: permutations with exactly two fixed points. | A000388 = Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-2 places. | A000389 = Binomial coefficients C(n,5). | A000390 = Number of 5-dimensional partitions of n. | A000391 = Euler transform of A000332. | A000392 = Stirling numbers of second kind S(n,3). | A000393 = Number of n-node rooted trees of height 6. | A000394 = Numbers of form x^2 + y^2 + 7z^2. | A000395 = 6th power of rooted tree enumerator; number of linear forests of 6 rooted trees. | A000396 = Perfect numbers n: n is equal to the sum of the proper divisors of n. | A000397 = Number of partitions into non-integral powers. | A000398 = Numbers of form x^2 + 2y^2 + 2yz + 4z^2. | A000399 = Unsigned Stirling numbers of first kind s(n,3).
| A000400 = Powers of 6. | A000401 = Numbers of form x^2 + y^2 + 2z^2. | A000402 = Number of permutations of [n] in which the longest increasing run has length 3. | A000403 = Number of simple equifacetted 3-manifolds with n faces. | A000404 = Numbers that are the sum of 2 nonzero squares. | A000405 = Number of 6-level labeled rooted trees with n leaves. | A000406 = Coefficients of iterated exponentials. | A000407 = (2n+1)!/n!. | A000408 = Numbers that are the sum of 3 nonzero squares. | A000409 = Singular n X n (0,1)-matrices: the number of n X n (0,1)-matrices having distinct, nonzero ordered rows, but having at least two equal columns or at least one zero column. | A000410 = Number of singular n X n rational (0,1)-matrices. | A000411 = Generalized tangent numbers d(6,n). | A000412 = Number of bipartite partitions of n white objects and 3 black ones. | A000413 = Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives A(A00092(n)). | A000414 = Numbers that are the sum of 4 nonzero squares. | A000415 = Numbers that are the sum of 2 but no fewer nonzero squares. | A000416 = Number of 6-dimensional partitions of n. | A000417 = Euler transform of A000389. | A000418 = Number of n-node rooted trees of height 7. | A000419 = Numbers that are the sum of 3 but no fewer nonzero squares. | A000420 = Powers of 7. | A000421 = Number of isomorphism classes of connected 3-regular loopless multigraphs of order 2n. | A000422 = Concatenation of numbers from n down to 1. | A000423 = a(n) is smallest number > a(n-1) of form a(i)a(j), i<j<n. | A000424 = Differences of reciprocals of unity. | A000425 = Coefficients of menage hit polynomials. | A000426 = Coefficients of menage hit polynomials. | A000427 = Number of 7-dimensional partitions of n. | A000428 = Euler transform of A000579. | A000429 = Number of n-node rooted trees of height 8. | A000430 = Primes and squares of primes. | A000431 = Expansion of 2*x^3/((1-2*x)^2*(1-4*x)). | A000432 = Series-parallel numbers. | A000433 = n written in base where place values are positive cubes. | A000434 = Number of permutations of [n] in which the longest increasing run has length 4. | A000435 = Normalized total height of rooted trees with n labeled nodes. | A000436 = Generalized Euler numbers c(3,n). | A000437 = Smallest nonnegative number that is the sum of 3 squares in exactly n ways. | A000438 = Number of 1-factorizations of K_{2n}. | A000439 = Powers of rooted tree enumerator. | A000440 = Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-4 places. | A000441 = Related to the divisor function. | A000442 = (n!)^3. | A000443 = Numbers that are the sum of 2 squares in exactly 3 ways. | A000444 = Partially labeled rooted trees with n nodes (3 of which are labeled). | A000445 = First occurrences of 2 consecutive n-th power residues. | A000446 = Smallest number that is the sum of 2 squares (allowing zeros) in exactly n ways. | A000447 = a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3. | A000448 = Smallest number that is the sum of 2 squares in at least n ways. | A000449 = Rencontres numbers: permutations with exactly 3 fixed points. | A000450 = Coefficients of menage hit polynomials. | A000451 = Smallest number that is the sum of 3 squares in at least n ways. | A000452 = a(n) is smallest number which avoids any 3-term geometric progression. | A000453 = Stirling numbers of the second kind, S(n,4). | A000454 = Unsigned Stirling numbers of first kind s(n,4). | A000455 = Digits of powers of 2. | A000456 = Number of permutations of [n] in which the longest increasing run has length 5. | A000457 = Exponential generating function: (1+3x)/(1-2x)^(7/2). | A000458 = a(0) = a(1) = 1; thereafter a(n) = sigma(a(n-1)) + sigma(a(n-2)). | A000459 = Number of permutations with no hits on 2 main diagonals. | A000460 = Eulerian numbers (Euler's triangle: column k=3 of A008292, column k=2 of A173018) | A000461 = Concatenate n n times. | A000462 = Numbers written in base of triangular numbers. | A000463 = n followed by n^2. | A000464 = Expansion of sin x /cos 2x. | A000465 = Number of bipartite partitions of n white objects and 4 black ones. | A000466 = 4*n^2 - 1. | A000467 = Number of permutations of [n] in which the longest increasing run has length 6. | A000468 = Powers of ten written in base 8. | A000469 = 1 together with products of >=2 distinct primes. | A000470 = Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-5 places. | A000471 = Floor( sinh(n ). | A000472 = a(n) = a(n-1)^2 + (a(n-2)+1)(a(n-1)-a(n-2)^2 ). | A000473 = Number of genus 0 rooted maps with 5 faces with n vertices | A000474 = Number of nonisomorphic 1-factorizations of K_{2n}. | A000475 = Rencontres numbers: permutations with exactly 4 fixed points. | A000476 = Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-1 places. | A000477 = Related to the divisor function. | A000478 = Number of ways of placing n labeled balls into 3 indistinguishable boxes with at least 2 balls in each box. | A000479 = Number of 1-factorizations of K_{n,n}. | A000480 = Floor(cos(n)). | A000481 = Stirling numbers of the second kind, S(n,5). | A000482 = Unsigned Stirling numbers of first kind s(n,5). | A000483 = Associated Stirling numbers: second order reciprocal Stirling numbers (Fekete) n \over 3. The number of 3-orbit permutations of an n-set with at least 2 elements in each orbit. | A000484 = Nearest integer to cos(n). | A000485 = Partially labeled trees with n nodes (4 of which are labeled). | A000486 = One half of the number of permutations of [n] such that the differences have 4 runs with the same signs. | A000487 = Number of permutations of length n with exactly two valleys. | A000488 = Generalized tangent numbers d_(n,3). | A000489 = Card matching. | A000490 = Generalized Euler numbers c(4,n). | A000491 = Number of bipartite partitions of n white objects and 5 black ones. | A000492 = Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-6 places. | A000493 = Floor(sin(n)). | A000494 = Nearest integer to sin(n). | A000495 = Nearest integer to sinh(n). | A000496 = Restricted permutations. | A000497 = S2(j,2j+2) where S2(n,k) is a 2-associated Stirling number of the second kind. | A000498 = Eulerian numbers (Euler's triangle: column k=4 of A008292, column k=3 of A173018) | A000499 = Related to the divisor function.
| A000500 = Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-7 places. | A000501 = Floor( cosh(n) ). | A000502 = Number of genus 0 rooted maps with 6 faces with n vertices | A000503 = Floor(tan(n)). | A000504 = S2(j,2j+3) where S2(n,k) is a 2-associated Stirling number of the second kind. | A000505 = Eulerian numbers (Euler's triangle: column k=5 of A008292, column k=4 of A173018) | A000506 = One half of the number of permutations of [n] such that the differences have 5 runs with the same signs. | A000507 = Number of permutations of [n] with exactly 3 increasing runs of length at least 2. | A000508 = Generalized class numbers. | A000509 = Size of second largest n-arc in PG(2,q), where q runs through the primes and prime powers >= 7. | A000510 = Maximal number of points in PG(2,q) with at most 3 on a line (next term is 21 or 22). | A000511 = Number of n-step spiral self-avoiding walks on hexagonal lattice, where at each step one may continue in same direction or make turn of 2pi/3 counterclockwise. | A000512 = Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 3, where equivalence is defined by row and column permutations. | A000513 = Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 4, where equivalence is defined by row and column permutations. Isomorphism classes of bicolored quartic bipartite graphs, where isomorphism cannot exchange the colors. | A000514 = Eulerian numbers (Euler's triangle: column k=6 of A008292, column k=5 of A173018) | A000515 = (2n)!(2n+1)!/n!^4, or equally (2n+1)C(2n,n)^2. | A000516 = Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 5, where equivalence is defined by row and column permutations. Isomorphism classes of bicolored 5-regular bipartite graphs, where isomorphism cannot exchange the colors. | A000517 = Number of permutations of length n with exactly three valleys. | A000518 = Generalized tangent numbers d_(n,4). | A000519 = Number of different row sums among Latin squares of order n. | A000520 = Nearest integer to log_10 (n). | A000521 = Coefficients of modular function j as power series in q = e^(2 Pi i t). | A000522 = Total number of arrangements of a set with n elements: a(n) = Sum_{k=0..n} n!/k!. | A000523 = Log_2(n) rounded down. | A000524 = Number of rooted trees with n nodes, 2 of which are labeled. | A000525 = Partially labeled rooted trees with n nodes (4 of which are labeled). | A000526 = Partially labeled trees with n nodes (5 of which are labeled). | A000527 = Series-parallel numbers. | A000528 = Number of types of Latin squares of order n. Equivalently, number of nonisomorphic 1-factorizations of K_{n,n}. | A000529 = Powers of rooted tree enumerator. | A000530 = Let p(n, s, x) be predicate that number of occurrences of s's in x >= 2*n - the length of the longest sequence of s's in x. Then a(n)=#{x in {0,1}* | x ends in 0 and p(n,0,x) and (there is no prefix y of x such that p(n,0,y) or p(n,1,y))}. | A000531 = From area of cyclic polygon of 2n + 1 sides. | A000532 = Number of Greek-key tours (walks) from NW corner of n X n array to SW corner. | A000533 = 10^n + 1, n >= 1. | A000534 = Numbers that are not the sum of 4 nonzero squares. | A000535 = Card matching. | A000536 = Number of 3-line Latin rectangles. | A000537 = Sum of first n cubes; or n-th triangular number squared. | A000538 = Sum of fourth powers: 0^4+1^4+...+n^4. | A000539 = Sum of 5th powers: 0^5 + 1^5 + 2^5 + ... + n^5. | A000540 = Sum of 6th powers: 1^6 + 2^6 + ... + n^6. | A000541 = Sum of 7th powers: 1^7 + 2^7 + ... + n^7. | A000542 = Sum of 8th powers: 1^8 + 2^8 + ... + n^8. | A000543 = Number of inequivalent ways to color vertices of a cube using at most n colors. | A000544 = Number of permutations of length n by rises. | A000545 = Number of ways of n-coloring a dodecahedron. | A000546 = First occurrence of n consecutive numbers that take same number of steps to reach 1 in 3x+1 problem. | A000547 = Number of steps to reach 1 in sequence A000546. | A000548 = Squares that are not the sum of 2 nonzero squares. | A000549 = Numbers that are the sum of 2 squares but not sum of 3 nonzero squares. | A000550 = Number of trees of diameter 7. | A000551 = Number of labeled rooted trees of height 2 with n nodes. | A000552 = Number of labeled rooted trees of height 3 with n nodes. | A000553 = Number of labeled rooted trees of height 4 with n nodes. | A000554 = Number of labeled trees of diameter 3 with n nodes. | A000555 = Number of labeled trees of diameter 4 with n nodes. | A000556 = Expansion of exp(-x) / (1 - exp(x) + exp(-x)). | A000557 = From Fibonacci sums. | A000558 = Generalized Stirling numbers of second kind. | A000559 = Generalized Stirling numbers of second kind. | A000560 = Number of ways of folding a strip of n labeled stamps. | A000561 = Number of discordant permutations. | A000562 = Number of discordant permutations. | A000563 = Number of discordant permutations. | A000564 = Number of discordant permutations. | A000565 = Number of discordant permutations. | A000566 = Heptagonal numbers (or 7-gonal numbers): n(5n-3)/2. | A000567 = Octagonal numbers: n*(3*n-2). Also called star numbers. | A000568 = Number of outcomes of unlabeled n-team round-robin tournaments. | A000569 = Number of graphical partitions of 2n. | A000570 = Number of tournaments on n nodes determined by their score vectors. | A000571 = Number of different scores that are possible in an n-team round-robin tournament. | A000572 = A Beatty sequence: [ n(e+1) ]. | A000573 = Number of 4 X n normalized Latin rectangles. | A000574 = Coefficient of x^5 in expansion of (1+x+x^2)^n. | A000575 = Tenth column of quintinomial coefficients. | A000576 = a(n) = number of (n-2) X n normalized Latin rectangles. | A000577 = Number of triangular polyominoes (or polyiamonds) with n cells (turning over is allowed, holes are allowed, must be connected along edges). | A000578 = The cubes: a(n) = n^3. | A000579 = Figurate numbers or binomial coefficients C(n,6). | A000580 = Binomial coefficients C(n,7). | A000581 = Binomial coefficients C(n,8). | A000582 = Binomial coefficients C(n,9). | A000583 = Fourth powers: a(n) = n^4. | A000584 = 5th powers: a(n) = n^5. | A000585 = Number of equivalence classes of Boolean functions of n variables under GL(n,2). | A000586 = Number of partitions of n into distinct primes. | A000587 = Rao Uppuluri-Carpenter numbers (or complementary Bell numbers): e.g.f. = exp(1 - exp(x)). | A000588 = 7*binomial(2n,n-3)/(n+4). | A000589 = 11*binomial(2n,n-5)/(n+6). | A000590 = 13*binomial(2n,n-6)/(n+7). | A000591 = Number of n-state 2-input 1-output automata with one initial and one terminal state. | A000592 = Number of nonnegative solutions of x^2 + y^2 = z in first n shells. | A000593 = Sum of odd divisors of n. | A000594 = Ramanujan's tau function (or tau numbers). | A000595 = Number of nonisomorphic unlabeled binary relations on n nodes. | A000596 = Central factorial numbers. | A000597 = Central factorial numbers. | A000598 = Number of rooted ternary trees with n nodes; number of n-carbon alkyl radicals C(n)H(2n+1) ignoring stereoisomers. | A000599 = Number of secondary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms.
| A000600 = Number of tertiary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms. | A000601 = Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)). | A000602 = Number of n-node unrooted quartic trees; number of n-carbon alkanes C(n)H(2n+2) ignoring stereoisomers. | A000603 = Number of nonnegative solutions to x^2 + y^2 <= n^2. | A000604 = Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2. | A000605 = Number of points of norm <= n in cubic lattice. | A000606 = Number of nonnegative solutions to x^2 + y^2 + z^2 <= n. | A000607 = Number of partitions of n into prime parts. | A000608 = Number of connected partially ordered sets with n unlabeled elements. | A000609 = Number of threshold functions of n or fewer variables. | A000610 = Number of self-complementary Boolean functions of n variables: see Comments for precise definition. | A000611 = Number of normalized Latin squares of order n containing no 2 X 2 Latin subsquare. | A000612 = Number of P-equivalence classes of switching functions of n or fewer variables, divided by 2. | A000613 = Number of Boolean functions of n variables. | A000614 = Complemented types of Boolean functions of n variables under action of AG(n,2). | A000615 = Threshold functions of exactly n variables. | A000616 = a(-1)=1 by convention; for n >= 0, a(n) = number of irreducible Boolean functions of n variables. | A000617 = Number of NP-equivalence classes of threshold functions of n or fewer variables. | A000618 = Nondegenerate Boolean functions of n variables. | A000619 = NP-equivalence classes of threshold functions of exactly n variable. | A000620 = Number of monosubstituted alkanes C(n-1)H(2n-1)-X with n-1 carbon atoms that are stereoisomers. | A000621 = Number of monosubstituted alkanes C(n-1)H(2n-1)-X with n-1 carbon atoms that are not stereoisomers. | A000622 = Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are stereoisomers. | A000623 = Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are stereoisomers. | A000624 = Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are not stereoisomers. | A000625 = Number of n-node steric rooted ternary trees; number of n carbon alkyl radicals C(n)H(2n+1) taking stereoisomers into account | A000626 = Number of stereoisomeric paraffins with n carbon atoms. | A000627 = Number of non-stereoisomeric paraffins with n carbon atoms. | A000628 = Number of n-node unrooted steric quartic trees; number of n-carbon alkanes C(n)H(2n+2) taking stereoisomers into account. | A000629 = Number of necklaces of partitions of n+1 labeled beads. | A000630 = Number of ways to represent n using the binary operator a * b = 2^a + b. | A000631 = Number of ethylene derivatives with n carbon atoms. | A000632 = Number of esters with n carbon atoms. | A000633 = Ammonium compounds with n carbon atoms. | A000634 = Glycols with n carbon atoms. | A000635 = Number of paraffins C_n H_{2n} X Y with n carbon atoms. | A000636 = Number of paraffins C_n H_{2n} X_2 with n carbon atoms. | A000637 = Number of fixed-point-free permutation groups of degree n. | A000638 = Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n. | A000639 = Alkyl benzenes with n carbon atoms: C(n)H(2n-6). | A000640 = Number of paraffins C_n H_{2n-1} XYZ with n carbon atoms. | A000641 = Number of paraffins C_n H_{2n-1} X_3 with n carbon atoms. | A000642 = Number of alkyl derivatives of acetylene X^{II} C_n H_{2n+2} with n carbon atoms. | A000643 = a(n)=a(n-1) + 2^a(n-2). | A000644 = Loops of length 4n on square grid that turn at each step and return to start in original direction. | A000645 = Number of alkyls X^{II} C_n H_{2n+1} Y with n carbon atoms. | A000646 = Number of alkyls Y^{II} C_n H_{2n+2} with n carbon atoms. | A000647 = Alkyl naphthalenes C_{n+10} H_{2n+8} with n+10 carbon atoms. | A000648 = Number of alkyls C_{n+15} H_{2n+10} (Anthr.) with n carbon atoms. | A000649 = Number of alkyls C_{n+15} H_{2n+10} (Phenan) with n carbon atoms. | A000650 = Number of alkyls S C_{n+4} H_{2n+4} with n carbon atoms. | A000651 = Running time of Takeuchi function. | A000652 = Invertible Boolean functions of n variables. | A000653 = Invertible Boolean functions of n variables. | A000654 = Invertible Boolean functions of n variables. | A000655 = a(n) = number of letters in a(n-1) (in English). | A000656 = Invertible Boolean functions of n variables with S(n) acting on the domain and GL(n,2) acting on the range. | A000657 = Median Euler numbers (the middle numbers of Arnold's shuttle triangle). | A000658 = Strehl's sequence "C_n^(3)". | A000659 = a(n) = 2^a(n-1) + a(n-2). | A000660 = Boustrophedon transform of 1,1,2,3,4,5,... | A000661 = Shifts 2 places left under boustrophedon transform. | A000662 = Relations with 3 arguments on n nodes. | A000663 = Relations on an infinite set. | A000664 = Number of graphs with n edges. | A000665 = Number of 3-uniform hypergraphs on n unlabeled nodes, or equivalently number of relations with 3 arguments on n nodes. | A000666 = Number of symmetric relations on n nodes. | A000667 = Boustrophedon transform of all-1's sequence. | A000668 = Mersenne primes (of form 2^p - 1 where p is a prime). | A000669 = Number of series-reduced planted trees with n leaves. Also the number of essentially series series-parallel networks with n edges; also the number of essentially parallel series-parallel networks with n edges. | A000670 = Number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements. | A000671 = Boron trees with n nodes = n-node rooted trees with deg <=3 at root and out-degree <=2 elsewhere. | A000672 = Number of 3-valent trees (= boron trees or binary trees) with n nodes. | A000673 = Number of bicentered 3-valent (or boron, or binary) trees with n nodes. | A000674 = Boustrophedon transform of 1,2,2,2,2,... | A000675 = Number of centered 3-valent (or boron, or binary) trees with n nodes. | A000676 = Number of centered trees with n nodes. | A000677 = Number of bicentered trees with n nodes. | A000678 = Number of carbon (rooted) trees with n carbon atoms = unordered 4-tuples of ternary trees. | A000679 = Number of groups of order 2^n. | A000680 = (2n)!/2^n. | A000681 = Number of n X n matrices with nonnegative entries and every row and column sum 2. | A000682 = Semimeanders: number of ways a semi-infinite directed curve can cross a straight line n times. | A000683 = Number of 2-colored labeled graphs on n nodes. | A000684 = Number of colored labeled n-node graphs with 2 interchangeable colors. | A000685 = Number of 3-colored labeled graphs on n nodes. | A000686 = Number of 4-colored labeled graphs on n nodes. | A000687 = Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,5,... | A000688 = Number of Abelian groups of order n; number of factorizations of n into prime powers. | A000689 = Final decimal digit of 2^n. | A000690 = Landau's approximation to population of x^2 + y^2. | A000691 = Ramanujan's approximation to population of x^2 + y^2. | A000692 = An approximation to population of x^2 + y^2. | A000693 = Related to population of numbers of form x^2 + y^2. | A000694 = Related to population of numbers of form x^2 + y^2. | A000695 = Moser-de Bruijn sequence: sums of distinct powers of 4. | A000696 = Numbers n such that (1,n) is "good". | A000697 = Boustrophedon transform of squares 1,1,4,9,16,... | A000698 = A problem of configurations: a(0) = 1; for n>0, a(n) = (2n-1)!! - Sum_{k=1..n-1} (2k-1)!! a(n-k). Also the number of shellings of an n-cube, divided by 2^n n!. | A000699 = Number of irreducible diagrams with 2n nodes.
| A000700 = Expansion of product (1+x^(2k+1)), k=0..inf; number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes. | A000701 = One half of number of non-self-conjugate partitions; also half of number of asymmetric Ferrers graphs with n nodes. | A000702 = a(n) = number of conjugacy classes in the alternating group A_n. | A000703 = Chromatic number (or Heawood number) of nonorientable surface with n crosscaps. | A000704 = Number of degree-n even permutations of order dividing 2. | A000705 = n-th superior highly composite number A002201(n) is product of first n terms of this sequence. | A000706 = Expansion of modular function 1/E_3 (cf. A013973). | A000707 = Number of permutations of [1,2,...,n] with n-1 inversions. | A000708 = a(n) = E(n+1)-2E(n), where E(i) is the Euler number A000111(i). | A000709 = Related to population of numbers of form x^2 + y^2. | A000710 = Number of partitions of n, with two kinds of 1,2,3 and 4. | A000711 = Number of partitions of n, with three kinds of 1,2,3 and 4 and two kinds of 5,6,7,... | A000712 = Number of partitions of n into parts of 2 kinds. | A000713 = EULER transform of 3, 2, 2, 2, 2, 2, 2, 2... | A000714 = Number of partitions of n, with three kinds of 1 and 2 and two kinds of 3,4,5,.... | A000715 = Number of partitions of n, with three kinds of 1,2 and 3 and two kinds of 4,5,6,.... | A000716 = Number of partitions of n into parts of 3 kinds. | A000717 = Number of graphs with n nodes and [ n(n-1)/4 ] edges. | A000718 = Boustrophedon transform of triangular numbers 1,1,3,6,10,... | A000719 = Number of disconnected graphs with n nodes. | A000720 = pi(n), the number of primes <= n. Sometimes called PrimePi(n) to distinguish it from the number 3.14159... | A000721 = Number of balanced Boolean functions of n variables. | A000722 = Invertible Boolean functions of n variables. | A000723 = Invertible Boolean functions of n variables. | A000724 = Invertible Boolean functions of n variables. | A000725 = Invertible Boolean functions of n variables. | A000726 = Number of partitions of n in which no parts are multiples of 3. | A000727 = Expansion of Product_{k >= 1} (1-x^k)^4. | A000728 = Expansion of Product (1-x^n)^5. | A000729 = Expansion of Product (1 - x^k)^6, k=1..inf. | A000730 = Expansion of Product (1-x^n )^7. | A000731 = Expansion of Product (1 - x^k)^8 in powers of x. | A000732 = Boustrophedon transform of primes 1,2,3,5,7,... | A000733 = Boustrophedon transform of partition numbers 1,1,1,2,3,5,7,... | A000734 = Boustrophedon transform of 1,1,2,4,8,16,32,... | A000735 = Expansion of Product (1-x^k)^(12). | A000736 = Boustrophedon transform of Catalan numbers 1,1,1,2,5,14,... | A000737 = Boustrophedon transform of natural numbers. | A000738 = Boustrophedon transform (second version) of Fibonacci numbers 0,1,1,2,3,... | A000739 = Expansion of Product (1-x^k )^16. | A000740 = Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement; also Dirichlet convolution of b_n=2^(n-1) with mu(n); also number of components of Mandelbrot set corresponding to Julia sets with an attractive n-cycle. | A000741 = Number of compositions of n into 3 ordered relatively prime parts. | A000742 = Number of compositions of n into 4 ordered relatively prime parts. | A000743 = Number of compositions of n into 5 ordered relatively prime parts. | A000744 = Boustrophedon transform (second version) of Fibonacci numbers 1,1,2,3,... ... | A000745 = Boustrophedon transform of squares. | A000746 = Boustrophedon transform of triangular numbers. | A000747 = Boustrophedon transform of primes. | A000748 = Expansion of bracket function. | A000749 = a(n)=4a(n-1)-6a(n-2)+4a(n-3), n > 3, with a(0)=a(1)=a(2)=0,a(3)=1. | A000750 = Expansion of bracket function. | A000751 = Boustrophedon transform of partition numbers. | A000752 = Boustrophedon transform of powers of 2. | A000753 = Boustrophedon transform of Catalan numbers. | A000754 = Boustrophedon transform of odd numbers. | A000755 = No-3-in-line problem on n X n grid: total number of ways of placing 2n points on n X n grid so no 3 are in a line. No symmetries are taken into account. | A000756 = Boustrophedon transform of sequence 1,1,0,0,0,0,... | A000757 = Number of cyclic permutations of [n] with no i->i+1 (mod n) | A000758 = Related to cumulative height of rooted plane trees. | A000759 = Number of n-step walks on cubic lattice. | A000760 = Number of n-step walks on cubic lattice. | A000761 = Number of n-step walks on cubic lattice. | A000762 = Number of n-step walks on cubic lattice. | A000763 = Number of interval orders constructed from n intervals of generic lengths. | A000764 = Boustrophedon transform of Bell numbers. | A000765 = Number of n-step walks on f.c.c. lattice. | A000766 = Number of n-step walks on f.c.c. lattice. | A000767 = Number of n-step walks on f.c.c. lattice. | A000768 = Number of n-step walks on f.c.c. lattice. | A000769 = No-3-in-line problem: number of inequivalent ways of placing 2n points on n X n grid so no 3 are in a line. | A000770 = Stirling numbers of the second kind, S(n,6). | A000771 = Stirling numbers of second kind, S(n,7). | A000772 = E.g.f. exp(tan(x) + sec(x) - 1). | A000773 = Number of numbers == 0 (mod 3) in range 2^n to 2^(n+1) with odd number of 1's in binary expansion. | A000774 = n!*(1+ Sum(i=1..n, 1/i )). | A000775 = n! * (n + 1 + 2*Sum_{k=1...n} 1/k). | A000776 = n! * (1 + 2*Sum_{k=1..n} 1/k). | A000777 = (n+2)*Catalan(n)-1. | A000778 = Catalan(n) + Catalan(n+1) - 1. | A000779 = 2*(2n-1)!!-(n-1)!*2^(n-1), where (2n-1)!! is A001147(n). | A000780 = (n+1)!/2+(n-1)(n-1)!. | A000781 = 3*Catalan(n)-Catalan(n-1)-1. | A000782 = 2*Catalan(n)-Catalan(n-1). | A000783 = Erroneous version of A007535. | A000784 = Symmetrical planar partitions of n: planar partitions (A000219) that when regarded as 3-D objects have just one symmetry plane). | A000785 = Number of asymmetrical planar partitions of n: planar partitions (A000219) that when regarded as 3-D objects have no symmetry). | A000786 = Number of planar partitions of n. | A000787 = Strobogrammatic numbers: the same upside down. | A000788 = Total number of 1's in binary expansions of 0, ..., n. | A000789 = Ramsey numbers. | A000790 = Primary pretenders: least composite c such that n^c == n (mod c). | A000791 = Ramsey numbers R(3,n). | A000792 = a(n) = max{ (n-i)*a(i) : i<n}; a(0) = 1. | A000793 = Landau's function g(n): largest order of permutation of n elements. Equivalently, largest lcm of partitions of n. | A000794 = Permanent of projective plane of order n. | A000795 = Salie numbers: expansion of cosh x / cos x = Sum_{n >= 0} a(n)*x^(2n)/(2n)!. | A000796 = Decimal expansion of Pi. | A000797 = Numbers that are not the sum of 4 tetrahedral numbers. | A000798 = Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements. | A000799 = Floor( 2^n /n ).
| A000800 = Sum of upward diagonals of Eulerian triangle. | A000801 = Sum_{k = 1..n} floor(2^k / k). | A000802 = Maximal number of states in deterministic finite automaton accepting a language consisting of some words of length n. | A000803 = a(n+3)=a(n+2)+a(n+1)+a(n)-4. | A000804 = Permanent of a certain cyclic n X n (0,1) matrix. | A000805 = Permanent of a certain cyclic n X n (0,1) matrix. | A000806 = Bessel polynomial y_n(-1). | A000807 = Quadratic invariants. | A000808 = Number of switching networks (see Harrison reference for precise definition). | A000809 = Number of switching networks (see Harrison reference for precise definition). | A000810 = Expansion of (sin x + cos x)/cos 3x. | A000811 = Number of switching networks (see Harrison reference for precise definition). | A000812 = Number of switching networks (see Harrison reference for precise definition). | A000813 = Expansion of (sin x + cos x)/cos 4x. | A000814 = Number of switching networks (see Harrison reference for precise definition). | A000815 = Number of switching networks (see Harrison reference for precise definition). | A000816 = E.g.f.: Sum_{n >= 0} a(n) * x^(2*n) / (2*n)! = sin(x)^2 / cos(2*x). | A000817 = Number of switching networks under action of GL_n(Z_2). | A000818 = Number of switching networks under action of GL_n(Z_2). | A000819 = Expansion of cos^2 x /cos 2x. | A000820 = Number of switching networks under action of AG_n(Z_2). | A000821 = Number of switching networks under action of AG_n(Z_2). | A000822 = Expansion of (sin^2 x + sin x ) /cos 2x. | A000823 = Number of switching networks (see Harrison reference for precise definition). | A000824 = Number of switching networks (see Harrison reference for precise definition). | A000825 = Expansion of cos x (1 + sin x ) /cos 2x. | A000826 = Number of switching networks (see Harrison reference for precise definition). | A000827 = Number of switching networks (see Harrison reference for precise definition). | A000828 = E.g.f. cos(x)/(cos(x) - sin(x)). | A000829 = Number of switching networks (see Harrison reference for precise definition). | A000830 = Number of switching networks (see Harrison reference for precise definition). | A000831 = E.g.f. (1 + tan(x))/(1 - tan(x)). | A000832 = Number of switching networks (see Harrison reference for precise definition). | A000833 = Number of switching networks (see Harrison reference for precise definition). | A000834 = Expansion of exp(x)(1+tan x)/(1-tan x). | A000835 = Number of switching networks (see Harrison reference for precise definition). | A000836 = Number of switching networks (see Harrison reference for precise definition). | A000837 = Number of partitions of n into relatively prime parts. Also aperiodic partitions. | A000838 = Number of n-input 2-output switching networks under action of complementing group on the inputs and outputs. | A000839 = Number of n-input 3-output switching networks under action of complementing group on the inputs and outputs. | A000840 = Number of cubic bicolored graphs admitting an automorphism exchanging the colors. | A000841 = Number of n-input 2-output switching networks under action of symmetric group S(n) on the inputs and complementing group C(2,2) on the outputs. | A000842 = Number of n-input 3-output switching networks under action of symmetric group S(n) on the inputs and complementing group C(3,2) on the outputs. | A000843 = Quartic bicolored graphs admitting an automorphism exchanging the colors. | A000844 = Number of switching networks (see Harrison reference for precise definition). | A000845 = Number of switching networks (see Harrison reference for precise definition). | A000846 = C(3n,n) - C(2n,n). | A000847 = Number of n-input 2-output switching networks under action of GL(n,2) on the inputs and complementing group C(2,2) on the outputs. | A000848 = Number of n-input 3-output switching networks under action of GL(n,2) on the inputs and complementing group C(3,2) on the outputs. | A000849 = Number of primes <= product of first n primes, A002110(n). | A000850 = Number of n-input 2-output switching networks under action of AG(n,2) on the inputs and complementing group C(2,2) on the outputs. | A000851 = Number of n-input 3-output switching networks under action of AG(n,2) on the inputs and complementing group C(3,2) on the outputs. | A000852 = Numbers beginning with a vowel. | A000853 = Number of n-input 2-output switching networks under action of complementing group C(2,n) on inputs and S(2) and C(2,2) on outputs | A000854 = Number of n-input 3-output switching networks under action of complementing group C(2,n) on inputs and S(3) and C(2,3) on outputs | A000855 = Final two digits of 2^n. | A000856 = Number of n-input 2-output switching networks under the action of S(n) on the inputs and S(2) and complementing group C(2,2) on the outputs | A000857 = Number of n-input 3-output switching networks under the action of S(n) on the inputs and S(3) and complementing group C(2,3) on the outputs | A000858 = Duplicate of A003436. | A000859 = Number of n-input 2-output switching networks under action of S(n) and complementing group C(2,2) on inputs and outputs | A000860 = Number of n-input 3-output switching networks under action of S(n) and complementing group C(2,3) on inputs and outputs | A000861 = Numbers ending with a vowel in American English. | A000862 = Number of n-input 2-output switching networks under action of AG(n,2) and complementing group C(2,2) on inputs and outputs | A000863 = Number of n-input 3-output switching networks under action of AG(n,2) and complementing group C(2,3) on inputs and outputs | A000864 = Deceptive nonprimes: composite numbers n such that n divides the repunit R_{n-1}. | A000865 = Numbers beginning with letter 'o'. | A000866 = 2^n written in base 5. | A000867 = Numbers beginning with letter 'f'. | A000868 = Number of switching networks with C(2,n) acting on domain and GL(2,Z2) acting on range. | A000869 = Number of switching networks with C(2,n) acting on domain and GL(3,Z2) acting on range. | A000870 = Numbers beginning with letter 's'. | A000871 = Number of switching networks with S(n) acting on the domain and GL(2,2) acting on the range. | A000872 = Number of switching networks with S(n) acting on the domain and GL(3,2) acting on the range. | A000873 = Numbers beginning with letter 'e'. | A000874 = Number of switching networks with S(n) and C(2,2) acting on the domain and GL(2,2) acting on the range. | A000875 = Number of switching networks with S(n) and C(2,2) acting on the domain and GL(3,2) acting on the range. | A000876 = From a self-replicating tiling. | A000877 = Number of switching networks with GL(n,2) acting on the domain and GL(2,2) acting on the range. | A000878 = Number of switching networks with GL(n,2) acting on the domain and GL(2,2) acting on the range. | A000879 = Number of primes < square of n-th prime. | A000880 = Number of switching networks with AG(n,2) acting on the domain and GL(2,2) acting on the range. | A000881 = Number of switching networks with AG(n,2) acting on the domain and GL(3,2) acting on the range. | A000882 = Number of twin prime pairs <= product of first n primes. | A000883 = Number of switching networks with C(2,n) actiong on the domain and AG(2,2) acting on the range. | A000884 = Number of switching networks with C(2,n) acting on the domain and AG(3,2) acting on the domain. | A000885 = Number of twin prime pairs < square of n-th prime. | A000886 = Number of switching networks with GL(n,2) acting on the domain and AG(2,2) acting on the range. | A000887 = Number of switching networks with GL(n,2) acting on the domain and AG(3,2) acting on the range. | A000888 = (2*n)!^2 / ((n+1)!*n!^3). | A000889 = Number of switching networks with S(n) and C(2,2) acting on the domain and AG(2,2) acting on the range. | A000890 = Number of switching networks with S(n) and C(2,2) acting on the domain and AG(2,3) acting on the range. | A000891 = (2*n)!*(2*n+1)! / (n! * (n+1)!)^2. | A000892 = Number of switching networks with GL(n,2) acting on the domain and AG(2,2) acting on the range. | A000893 = Number of switching networks with GL(n,2) acting on the domain and AG(3,2) acting on the range. | A000894 = (2*n)!*(2*n+1)! /((n+1)! *n!^3). | A000895 = Number of switching networks with AG(n,2) acting on the domain and AG(2,2) acting on the range. | A000896 = Number of switching networks with AG(n,2) acting on the domain and AG(3,2) acting on the range. | A000897 = (4n)! / ((2n)! n!^2). | A000898 = a(n) = 2(a(n-1) + (n-1)a(n-2)). | A000899 = Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
| A000900 = Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details). | A000901 = Number of solutions to the rook problem on a 2n X 2n board having a certain symmetry group (see Robinson for details). | A000902 = E.g.f.: (1/2)*(exp(2x + x^2) + 1). | A000903 = Number of inequivalent ways of placing n nonattacking rooks on n X n board. | A000904 = a(n) = (n + 1) a(n - 1) + (n + 2) a(n - 2) + a(n - 3); a(1)=0, a(2)=3, a(3)=13. | A000905 = Hamilton numbers. | A000906 = Exponential generating function: 2(1+3x)/(1-2x)^(7/2). | A000907 = Second order reciprocal Stirling number (Fekete) 2n+2 \over n. The number of n-orbit permutations of a (2n+2)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g. Comtet). | A000908 = Atom-rooted polyenoids with n edges. | A000909 = (2n)!(2n+1)! / n!^2. | A000910 = 5*C(n,6). | A000911 = (2n+3)! /( n! * (n+1)! ). | A000912 = Expansion of (sqrt(1-4x^2)-sqrt(1-4x))/(2x). | A000913 = Number of bond-rooted polyenoids with n edges. | A000914 = Stirling numbers of first kind: s(n+2,n). | A000915 = Stirling numbers of first kind s(n+4,n). | A000916 = a(2n) = n+2, a(2n-1) = smallest number requiring n+2 letters in English. | A000917 = (2n+3)!/(n!*(n+2)!). | A000918 = 2^n - 2. | A000919 = 4^n - C(4,3)*3^n + C(4,2)*2^n - C(4,1). | A000920 = Differences of 0: 6!*S(n,6). | A000921 = Primes p of the form 3k+1 such that the sum(x=1 to p) of cos(2*pi*x^3/p) is greater than sqrt(p). | A000922 = Primes p of the form 3k+1 such that the sum(x=1 to p) of cos(2*pi*x^3/p) is between -sqrt(p) and +sqrt(p). | A000923 = Primes p of the form 3k+1 such that the sum(x=1 to p) of cos(2*pi*x^3/p) is less than -sqrt(p). | A000924 = Class number of Q(sqrt(-n)), n squarefree. | A000925 = Number of ordered ways of writing n as a sum of 2 squares of nonnegative integers. | A000926 = Euler's "numerus idoneus" (idoneal, or suitable, or convenient numbers). | A000927 = "First factor" (or relative class number) h- for cyclotomic field Q( exp(2 Pi / prime(n)) ). | A000928 = Irregular primes: p is regular if and only if the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) are not divisible by p. | A000929 = Dimension of n-th degree part of Steenrod algebra. | A000930 = Narayana's cows sequence: a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) + a(n-3). | A000931 = Padovan sequence: a(n) = a(n-2) + a(n-3) with a(0)=1, a(1)=a(2)=0. | A000932 = a(n) = a(n-1) + n*a(n-2); a(0) = a(1) = 1. | A000933 = Genus of complete graph on n nodes. | A000934 = Chromatic number (or Heawood number) Chi(n) of surface of genus n. | A000935 = Number of free planar polyenoids with 2n nodes. | A000936 = Number of free planar polyenoids with n nodes. | A000937 = Length of longest simple cycle without chords in the n-dimensional hypercube graph. Also called n-coil or closed n-snake-in-the-box problem. | A000938 = Number of collinear point-triples in an n X n grid. | A000939 = Number of inequivalent n-gons. | A000940 = Number of n-gons with n vertices. | A000941 = Number of free planar polyenoids with n nodes. | A000942 = Number of free planar polyenoids with n nodes. | A000943 = Number of combinatorial types of simplicial n-dimensional polytopes with n+3 nodes. | A000944 = Number of polyhedra (or 3-connected simple planar graphs) with n nodes. | A000945 = Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of Product_{k=1..n} a(k) + 1. | A000946 = Euclid-Mullin sequence: a(1) = 2, a(n+1) is largest prime factor of Product_{k=1..n} a(k) + 1. | A000947 = Number of free nonplanar polyenoids with n nodes. | A000948 = Number of free nonplanar polyenoids with n nodes. | A000949 = Number of forests with n nodes and height at most 2. | A000950 = Number of forests with n nodes and height at most 3. | A000951 = Number of forests with n nodes and height at most 4. | A000952 = Orders n == 2 (mod 4) of conference matrices. | A000953 = Number of free nonplanar polyenoids with n nodes. | A000954 = Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways. | A000955 = A sequence satisfying (a(2n+1)+1)^3 = sum(a(k)^3,k=1..2n+1) | A000956 = A sequence satisfying (a(2n+1)+1)^3 = sum(a(k)^3,k=1..2n+1) | A000957 = Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree. | A000958 = Number of ordered rooted trees with n edges having root of odd degree. | A000959 = Lucky numbers. | A000960 = Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate. | A000961 = Prime powers p^k (p prime, k >= 0). | A000962 = A ternary continued fraction. | A000963 = A ternary continued fraction. | A000964 = A ternary continued fraction. | A000965 = Numerators of expansion of sinh x / sin x. | A000966 = n! never ends in this many 0's. | A000967 = Sum of Fermat coefficients. | A000968 = Sum of odd Fermat coefficients rounded to nearest integer. | A000969 = G.f.: (1+x+2*x^2)/((1-x)^2*(1-x^3)). | A000970 = Fermat coefficients. | A000971 = Fermat coefficients. | A000972 = Fermat coefficients. | A000973 = Fermat coefficients. | A000974 = Conjecturally the number of even integers the sum of two primes in exactly n ways. | A000975 = a(2n) = 2*a(2n-1), a(2n+1) = 2*a(2n)+1 (also n-th number without consecutive equal binary digits). | A000976 = Period of 1 / n! in base 10. | A000977 = Numbers that are divisible by at least three different primes. | A000978 = Wagstaff numbers: numbers n such that (2^n + 1)/3 is prime. | A000979 = Wagstaff primes: primes of form (2^p + 1)/3. | A000980 = Number of ways of writing 0 as Sum_{k=-n..n} e(k)*k, where e(k) is 0 or 1. | A000981 = Numbers beginning with letter 'n'. | A000982 = Ceiling(n^2/2). | A000983 = Size of minimal covering code of length n and covering radius 1 (the next term is in the range 105-120). | A000984 = Central binomial coefficients: C(2*n,n) = (2*n)!/(n!)^2. | A000985 = Number of n X n symmetric matrices with nonnegative entries and all row sums 2. | A000986 = Number of n X n symmetric matrices with (0,1) entries and all row sums 2. | A000987 = Number of stochastic matrices of integers. | A000988 = Number of one-sided polyominoes with n cells. | A000989 = 3^a(n) divides C(2n,n). | A000990 = Number of plane partitions of n with at most two rows. | A000991 = Number of 3-line partitions of n. | A000992 = "Half-Catalan numbers": a(n) = Sum_{k=1 ... floor(n/2)} a(k)a(n-k) with a(1) = 1. | A000993 = Number of distinct quadratic residues mod 10^n = number of distinct n-digit endings of base 10 squares. | A000994 = Shifts 2 places left under binomial transform. | A000995 = Shifts left two terms under the binomial transform. | A000996 = Shifts 3 places left under binomial transform. | A000997 = From a differential equation. | A000998 = From a differential equation. | A000999 = 5^a(n) divides C(2n,n).
