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A035999 Number of partitions of n into parts not of the form 23k, 23k+11 or 23k-11. Also number of partitions with at most 10 parts of size 1 and differences between parts at distance 10 are greater than 1. 1
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 98, 130, 168, 219, 279, 359, 453, 575, 720, 904, 1122, 1397, 1722, 2125, 2603, 3190, 3883, 4729, 5725, 6930, 8349, 10053, 12053, 14444, 17243, 20569, 24457, 29055, 34414, 40728, 48070, 56683, 66682 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Andrews-Gordon Identity

FORMULA

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

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+11-23))*(1 - x^(23*k-11))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A008639 A008633 A238868 * A036010 A328545 A192061

Adjacent sequences:  A035996 A035997 A035998 * A036000 A036001 A036002

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

a(0)=1 prepended by Seiichi Manyama, May 10 2018

STATUS

approved

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Last modified September 25 22:55 EDT 2020. Contains 337346 sequences. (Running on oeis4.)