A035968 Number of partitions of n into parts not of the form 17k, 17k+7 or 17k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 7 are greater than 1.

1, 2, 3, 5, 7, 11, 14, 21, 28, 38, 50, 68, 87, 115, 147, 190, 240, 307, 383, 484, 601, 749, 923, 1143, 1397, 1715, 2086, 2541, 3073, 3722, 4476, 5390, 6454, 7728, 9212, 10983, 13035, 15471, 18295, 21624, 25478, 30005, 35229, 41344, 48393, 56602

Offset

1,2

Comments

Case k=8,i=7 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Table of n, a(n) for n=1..46.

Formula

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

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 7-17))*(1 - x^(17*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A055803 A023027 A051014 * A112581 A288255 A325853

Adjacent sequences: A035965 A035966 A035967 * A035969 A035970 A035971

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved