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, 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

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: A008632 A347575 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