Template:Sequence/list/names/A000000..A000999/doc

This documentation subpage contains instructions, categories, or other information for Template:Sequence/list/names/A000000..A000999. [<Edit> Template:Sequence/list/names/A000000..A000999]

[⧼Purge⧽ Template:Sequence/list/names/A000000..A000999/doc]

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 &#x007C; 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.)

Usage

{{sequence/list/names/A000000..A000999|A-number = A-number}}

or

{{sequence/list/names/A000000..A000999|A-number}}

or

{{seq/list/names/A000000..A000999|A-number = A-number}}

or

{{seq/list/names/A000000..A000999|A-number}}

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 &#x007C; 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.