A035956 Number of partitions of n into parts not of the form 15k, 15k+2 or 15k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 6 are greater than 1.
1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 44, 57, 73, 93, 116, 147, 183, 228, 282, 348, 426, 524, 637, 775, 939, 1136, 1366, 1645, 1969, 2356, 2809, 3345, 3969, 4709, 5564, 6570, 7739, 9105, 10683, 12527, 14651, 17120, 19965, 23257, 27039, 31412, 36420
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+ 2-15))*(1 - x^(15*k- 2))/(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(2*Pi/15) / (15^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
Comments