A035978 Number of partitions of n into parts not of the form 19k, 19k+9 or 19k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 8 are greater than 1.

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 53, 72, 93, 123, 158, 205, 260, 333, 418, 529, 659, 824, 1019, 1264, 1551, 1908, 2328, 2843, 3448, 4185, 5048, 6092, 7313, 8777, 10489, 12531, 14910, 17733, 21019, 24896, 29399, 34692, 40824, 48004, 56307

Offset

0,3

Comments

Case k=9,i=9 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(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 09 2018

Mathematica

nmax = 50; CoefficientList[Series[Product[((1 - x^(19*k))*(1 - x^(19*k - 9))*(1 - x^(19*k - 10)))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 09 2018 *)

Crossrefs

Sequence in context: A008631 A347574 A238866 * A319475 A319454 A023029

Adjacent sequences: A035975 A035976 A035977 * A035979 A035980 A035981

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

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

Status

approved