A035955 Number of partitions in parts not of the form 15k, 15k+1 or 15k-1. Also number of partitions with no part of size 1 and differences between parts at distance 6 are greater than 1.
0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 33, 40, 53, 64, 84, 100, 129, 155, 195, 234, 293, 349, 431, 515, 629, 748, 909, 1076, 1298, 1535, 1837, 2166, 2582, 3032, 3595, 4214, 4972, 5810, 6831, 7959, 9321, 10837, 12643, 14662, 17057, 19728, 22880, 26409
Offset: 1
References
- G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
Programs
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Mathematica
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(15*k))*(1 - x^(15*k+ 1-15))*(1 - x^(15*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
Formula
a(n) ~ exp(2*Pi*sqrt(2*n/15)) * 2^(1/4) * sin(Pi/15) / (15^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
Comments