A035969 Number of partitions of n into parts not of the form 17k, 17k+8 or 17k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 7 are greater than 1.

1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 39, 51, 69, 89, 117, 150, 194, 245, 313, 392, 494, 614, 766, 944, 1168, 1430, 1754, 2135, 2601, 3146, 3810, 4585, 5519, 6611, 7917, 9440, 11253, 13361, 15856, 18755, 22169, 26124, 30766, 36132, 42401, 49639, 58063

Offset

0,3

Comments

Case k=8,i=8 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) ~ exp(2*Pi*sqrt(7*n/51)) * 7^(1/4) * cos(Pi/34) / (3^(1/4) * 17^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 8-17))*(1 - x^(17*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A347573 A238865 A326978 * A355027 A332745 A042953

Adjacent sequences: A035966 A035967 A035968 * A035970 A035971 A035972

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

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

Status

approved