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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 08:20 EDT 2020. Contains 336201 sequences. (Running on oeis4.)