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A035988 Number of partitions of n into parts not of the form 21k, 21k+10 or 21k-10. Also number of partitions with at most 9 parts of size 1 and differences between parts at distance 9 are greater than 1. 1
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 54, 74, 96, 127, 164, 213, 271, 348, 438, 555, 694, 869, 1077, 1339, 1647, 2029, 2482, 3036, 3690, 4487, 5423, 6555, 7886, 9480, 11350, 13583, 16191, 19287, 22902, 27169, 32138, 37984, 44772, 52726, 61948 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Case k=10,i=10 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(n/7)) * cos(Pi/42) / (sqrt(3) * 7^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+10-21))*(1 - x^(21*k-10))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A008638 A008632 A238867 * A088669 A091580 A325857

Adjacent sequences:  A035985 A035986 A035987 * A035989 A035990 A035991

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 June 25 08:27 EDT 2021. Contains 345453 sequences. (Running on oeis4.)