A035997 Number of partitions of n into parts not of the form 23k, 23k+9 or 23k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 10 are greater than 1.

1, 2, 3, 5, 7, 11, 15, 22, 29, 41, 54, 74, 96, 127, 164, 214, 272, 350, 441, 560, 700, 879, 1090, 1357, 1671, 2062, 2524, 3093, 3762, 4581, 5543, 6709, 8078, 9725, 11655, 13965, 16664, 19875, 23623, 28060, 33225, 39314, 46388, 54691, 64320

Offset

1,2

Comments

Case k=11,i=9 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Table of n, a(n) for n=1..45.

Formula

a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * cos(5*Pi/46) / (3^(1/4) * 23^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+ 9-23))*(1 - x^(23*k- 9))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A023029 A358909 A035987 * A036008 A104502 A027343

Adjacent sequences: A035994 A035995 A035996 * A035998 A035999 A036000

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved