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User:Mitch Harris

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I am a computer scientist currently working in medical informatics. My education has been in computer science all the way back.

I have many mathematical interests, including combinatorial enumeration and binomial identities, and these are reflected in my handful of submissions to the OEIS.

If you google for me, I am not a thrash metal punk rocker, a lawyer, a contractor, or a devastating hurricane.

My OEIS opinions on sequences are generally (reserving the right to be inconsistent):

- anything with base 10 is suspect (except when it generalizes to any base), except for base 2.
- I personally don't care for things having to do with primes. Sorry, I just don't care.
- almost always a(0) = 1 for combinatorial things, which includes 0^0.

My favorite sequences:

OEIS description sequence
A000027 The natural numbers. Also called the whole numbers, the counting numbers or the positive integers.
A000001 Number of groups of order n.
A000595 Nonisomorphic unlabeled binary relations on n nodes.
A000372 Dedekind numbers: monotone Boolean functions or antichains of subsets of an n-set.
A000133 Boolean functions of n variables.
A000157 Boolean functions of n variables.
A000613 Boolean functions of n variables.
A000142 Factorial numbers: n! = 1*2*3*4*...*n (order of symmetric group S_n, number of permutations of n letters).
A000111 Euler or up/down numbers: expansion of sec x + tan x . Also alternating permutations on n letters.
A000139 2-stack sortable permutations on n letters.
A000166 Subfactorial or rencontres numbers, or derangements: permutations of n elements with no fixed points.
A000240 Rencontres numbers: permutations with exactly one fixed point.
A000085 Self-inverse permutations on n letters; Young tableaux with n cells.
A000364 Euler (or secant or "Zig") numbers: expansion of sec x.
A000140 Kendall-Mann numbers: maximal inversions in permutation of n letters.
A000029 Necklaces with n beads of 2 colors, allowing turning over.
A000031 n-bead necklaces with 2 colors when turning over is not allowed; output sequences from a simple n-stage cycling shift register; binary irreducible polynomials whose degree divides n.
A000041 a(n) = number of partitions of n (the partition numbers).
A000100 Compositions.
A000102 Compositions.
A000110 Bell or exponential numbers: ways of placing n labeled balls into n indistinguishable boxes.
A000123 Binary partitions: number of partitions of 2n into powers of 2.
A000219 Planar partitions of n.
A000079 Powers of 2: a(n) = 2^n.
A000165 Double factorial numbers: (2n)!! = 2^n*n!.
A000045 Fibonacci numbers: F(n) = F(n-1) + F(n-2), F(0) = 0, F(1) = 1, F(2) = 1, ...
A000032 Lucas numbers (beginning at 2): L(n) = L(n-1) + L(n-2).
A000073 Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3).
A000213 Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3).
A000108 Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!). Also called Segner numbers.
A000063 Symmetrical dissections of an n-gon.
A000131 Asymmetrical dissections of n-gon.
A000060 Signed trees with n nodes.
A000081 Rooted trees with n nodes (or connected functions with a fixed point).
A000107 Rooted trees with n nodes and a single labeled node; pointed rooted trees; vertebrates.
A000087 Rooted planar maps.
A000365 Rooted planar maps with n edges.
A000305 Rooted planar maps.
A000109 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.
A000151 Oriented rooted trees with n nodes. Also rooted trees with n nodes and 2-colored non-root nodes.
A000169 Labeled rooted trees with n nodes: n^(n-1).
A000272 Labeled trees on n nodes: n^(n-2).
A000220 Asymmetric trees with n nodes (also called identity trees).
A000254 Stirling numbers of first kind s(n,2): a(n+1)=(n+1)*a(n)+n!.
A000453 Stirling numbers of second kind.
A000088 Graphs with n nodes.
A000171 Self-complementary graphs with n nodes.
A000282 Finite automata.
A000112 Partially ordered sets ("posets") with n unlabeled elements.
A000137 Series-parallel numbers.
A007814 Exponent of highest power of 2 dividing n (the binary carry sequence) 0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,...


A006519 Highest power of 2 dividing n. 1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,32,...


A002620 Quarter-squares: floor(n/2)*ceiling(n/2). Equivalently, floor(n^2/4). 0,0,1,2,4,6,9,12,16,20,25,30,36,42,49,56,64,72,81,90,100...


A003042 Number of Hamiltonian cycles (or Gray codes) on n-cube. 1,2,12,2688,1813091520


A003188 Decimal equivalent of Gray code for n. 0,1,3,2,6,7,5,4,12,13,15,14,10,11,9,8,24,25,27,26,30,31,29,


A002487 Stern's diatomic series: a(0) = 0, a(1) = 1; for n >= 1, a(2n) = a(n), a(2n+1) = a(n) + a(n+1). 0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,


A001175 Pisano periods (or Pisano numbers): period of Fibonacci numbers mod n. 1,3,8,6,20,24,16,12,24,60,10,24,28,48,40,24,36,24,18,60,16...


A006345 Linus sequence: a(n) "breaks the pattern" by avoiding the longest doubled suffix. 1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1,2,1,1,1,2,2,1,2,1,1,2,2,1,1,


A008302 Triangle of Mahonian (inversion) numbers T(n,k): coefficients in expansion of Product (1+x+...+x^k); k=0..n. 1,1,1,1,2,2,1,1,3,5,6,5,3,1,1,4,9,15,20,22,20,15,9,4,1,1,5,


A008280 Boustrophedon version of triangle of Euler-Bernoulli or Entringer numbers read by rows 1,0,1,1,1,0,0,1,2,2,5,5,4,2,0,0,5,10,14,16,16,61,61,56,46, 32,16,0,0,61,122,178,224,256,272,272,1385,1385,1324,1202, 1024,800,544,272,0,


A000111 Euler or up/down numbers: expansion of sec x + tan x . Also alternating permutations on n letters. 1,1,1,2,5,16,61,272,1385,7936,50521,353792,2702765,22368256,


A000085 Number of self-inverse permutations on n letters; number of Young tableaux with n cells. 1,1,2,4,10,26,76,232,764,2620,9496,35696,140152,568504,

My submissions (so actually not necessarily my favorites): (or get all at once)

A056932 A056932-A056937 Antichains in posets 1,20,168,887,3490,11196,30900,75966,170379,354640,693836


A057347 A057347-A057350 Calendar sequences 2, 5, 7, 10, 13, 16, 18, 21, 24, 26...


A057353 A057353-A057367 Floor(2n/5) (and other Beatty sequences of some rationals) 0,0,0,1,1,2,2,2,3,3,4,4,4,5,5,6,6,6,7,7,8,8,8,9,9,10,10,10...


A059176 A059176-A059200 Engel expansions of some constants 1, 1, 5, 6, 13, 16, 16, 38, 48, 58, 104, 177...


A059531 A059531-A059569 More Beatty sequences (mostly irrationals) 1,2,3,5,6,7,9,10,11,13,14,15,17,18,19,21,22,23,25,26,27,29,


A102378 A102378-A102379 Mixed linear and divconq recurrences 1, 3, 5, 9, 13, 19, 25, 35, 45, 59, 73...


A102894 A102894-A102897 Number of ACI algebras 1,1,4,45,2271,1373701,75965474236...


A109004 A109004-A109015,A109042-A109054 GCD and LCM sequences 0, 1, 1, 2, 1, 2, 3, 1, 1, 3, 4, 1, 2, 1, 4, 5, 1, 1, 1, 1, 5, 6, 1, 2, 3, 2, 1, 6, 7...


A109498 A109498-A109502 Number of closed walks of length 2n on the Heawood Graph... 1, 3, 15, 111, 951, 8463, 75975, 683391...


A114714 A114714-A114717 Linear Extensions 1, 2, 48, 2452, 183958, 17454844, 1941406508...
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