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
References
- G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
Programs
-
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 *)
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
Comments