A035971 Number of partitions of n into parts not of the form 19k, 19k+2 or 19k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 8 are greater than 1.

1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 75, 96, 120, 153, 191, 239, 297, 368, 453, 559, 683, 834, 1015, 1233, 1489, 1800, 2164, 2599, 3112, 3720, 4432, 5278, 6262, 7422, 8777, 10365, 12208, 14368, 16869, 19783, 23157, 27073, 31591, 36831

Offset

1,3

Comments

Case k=9,i=2 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..48.

Formula

a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * sin(2*Pi/19) / (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+ 2-19))*(1 - x^(19*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A105782 A035956 A035963 * A035980 A035990 A036001

Adjacent sequences: A035968 A035969 A035970 * A035972 A035973 A035974

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved