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:
|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).|
|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.|
|A000112||Partially ordered sets ("posets") with n unlabeled elements.|
|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...|