A035990 Number of partitions of n into parts not of the form 23k, 23k+2 or 23k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 10 are greater than 1.

1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 75, 96, 121, 154, 193, 242, 301, 374, 461, 570, 698, 854, 1042, 1268, 1535, 1859, 2240, 2696, 3235, 3875, 4627, 5521, 6565, 7797, 9240, 10934, 12906, 15220, 17907, 21043, 24683, 28915, 33811, 39497

Offset

1,3

Comments

Case k=11,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(2*Pi*sqrt(10*n/69)) * 10^(1/4) * sin(2*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+ 2-23))*(1 - x^(23*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035963 A035971 A035980 * A036001 A027336 A237830

Adjacent sequences: A035987 A035988 A035989 * A035991 A035992 A035993

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved