A035996 Number of partitions of n into parts not of the form 23k, 23k+8 or 23k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 10 are greater than 1.

1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 72, 94, 124, 160, 208, 265, 340, 429, 543, 680, 852, 1057, 1314, 1619, 1995, 2443, 2990, 3638, 4426, 5356, 6477, 7800, 9384, 11246, 13467, 16070, 19156, 22769, 27032, 32006, 37857, 44665, 52640, 61904

Offset

1,2

Comments

Case k=11,i=8 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(7*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+ 8-23))*(1 - x^(23*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A101049 A333193 A035986 * A261775 A036007 A027342

Adjacent sequences: A035993 A035994 A035995 * A035997 A035998 A035999

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved