A035989 Number of partitions in parts not of the form 23k, 23k+1 or 23k-1. Also number of partitions with no part of size 1 and differences between parts at distance 10 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 209, 252, 318, 381, 474, 569, 700, 837, 1024, 1219, 1480, 1760, 2120, 2514, 3015, 3561, 4248, 5008, 5944, 6986, 8261, 9680, 11402, 13331, 15641, 18240, 21338, 24817, 28941

Offset

1,4

Comments

Case k=11,i=1 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..50.

Formula

a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * sin(Pi/23) / (3^(1/4) * 23^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+ 1-23))*(1 - x^(23*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A240017 A035979 A240018 * A240019 A036000 A002865

Adjacent sequences: A035986 A035987 A035988 * A035990 A035991 A035992

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved