A035977 Number of partitions of n into parts not of the form 19k, 19k+8 or 19k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 8 are greater than 1.

1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 52, 71, 92, 121, 156, 202, 256, 328, 412, 520, 649, 811, 1002, 1243, 1526, 1875, 2289, 2794, 3388, 4112, 4960, 5982, 7183, 8619, 10299, 12302, 14638, 17404, 20630, 24431, 28848, 34038, 40053, 47088, 55234

Offset

1,2

Comments

Case k=9,i=8 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..45.

Formula

a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(3*Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 8-19))*(1 - x^(19*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A246579 A232480 A332638 * A288256 A101049 A333193

Adjacent sequences: A035974 A035975 A035976 * A035978 A035979 A035980

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved