A035943 Number of partitions of n into parts not of the form 9k, 9k+4 or 9k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 3 are greater than 1.

1, 1, 2, 3, 4, 5, 8, 10, 14, 18, 24, 30, 40, 49, 63, 78, 98, 120, 150, 182, 224, 271, 330, 396, 480, 572, 687, 817, 974, 1151, 1367, 1608, 1898, 2226, 2614, 3053, 3573, 4157, 4844, 5620, 6524, 7544, 8731, 10066, 11611, 13353, 15356, 17612, 20203, 23112

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Case k=4,i=4 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

Programs

Mathematica

nmax = 60; CoefficientList[Series[Product[1 / ((1 - x^(9*k-1)) * (1 - x^(9*k-2)) * (1 - x^(9*k-3)) * (1 - x^(9*k-6)) * (1 - x^(9*k-7)) * (1 - x^(9*k-8)) ), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 12 2015 *)

Formula

a(n) ~ cos(Pi/18) * exp(2*Pi*sqrt(n)/3) / (3*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Nov 12 2015

Extensions

a(0)=1 prepended by Seiichi Manyama, May 08 2018