User:Mitch Harris

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...