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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A319454 A023029 A035987 * A036008 A104502 A027343

Adjacent sequences:  A035994 A035995 A035996 * A035998 A035999 A036000

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 4 18:27 EDT 2020. Contains 336202 sequences. (Running on oeis4.)