A035957 Number of partitions in parts not of the form 15k, 15k+3 or 15k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 6 are greater than 1.
1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 46, 58, 77, 96, 125, 155, 198, 244, 308, 378, 471, 574, 709, 860, 1053, 1270, 1544, 1854, 2239, 2676, 3213, 3824, 4567, 5414, 6435, 7600, 8993, 10584, 12474, 14632, 17180, 20088, 23505, 27403, 31960, 37154
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+ 3-15))*(1 - x^(15*k- 3))/(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)) * sqrt(5 - sqrt(5)) / (2^(5/4) * 15^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
Comments