A035976 Number of partitions of n into parts not of the form 19k, 19k+7 or 19k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 8 are greater than 1.

1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 69, 89, 118, 151, 196, 248, 318, 398, 504, 627, 784, 968, 1201, 1472, 1811, 2207, 2695, 3266, 3964, 4777, 5764, 6916, 8299, 9912, 11840, 14080, 16744, 19837, 23492, 27730, 32717, 38485, 45246, 53055, 62167

Offset

1,2

Comments

Case k=9,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(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(5*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+ 7-19))*(1 - x^(19*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A112581 A288255 A325853 * A035985 A035995 A036006

Adjacent sequences: A035973 A035974 A035975 * A035977 A035978 A035979

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved