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

0,3

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

Formula

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

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 *)

Crossrefs

Sequence in context: A238479 A035562 A107234 * A240177 A035555 A039875

Adjacent sequences: A035940 A035941 A035942 * A035944 A035945 A035946

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

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

Status

approved