A280953 Expansion of Product_{k>=0} 1/(1 - x^(3*k*(k+1)+1)).
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 22, 23, 24, 25, 25, 27, 27, 29, 30, 31, 32, 32, 34, 34, 36, 37, 38, 39, 40, 43, 44, 46, 47, 48, 50, 51, 54, 55, 57, 58, 59
Offset: 0
Keywords
Examples
a(14) = 3 because we have [7, 7], [7, 1, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..20000
- M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
- M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
- Eric Weisstein's World of Mathematics, Hex Number
- Index entries for sequences related to centered polygonal numbers
- Index entries for related partition-counting sequences
Programs
-
Maple
h:= proc(n) option remember; `if`(n<0, 0, (t-> `if`(3*t*(t+1)+1>n, t-1, t))(1+h(n-1))) end: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0, b(n, i-1)+(t-> b(n-t, min(i, h(n-t))))(3*i*(i+1)+1))) end: a:= n-> b(n, h(n)): seq(a(n), n=0..100); # Alois P. Heinz, Dec 28 2018 -
Mathematica
nmax = 86; CoefficientList[Series[Product[1/(1 - x^(3 k (k + 1) + 1)), {k, 0, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Product_{k>=0} 1/(1 - x^(3*k*(k+1)+1)).
Comments