login
A035953
Number of partitions of n into parts not of the form 13k, 13k+5 or 13k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 5 are greater than 1.
5
1, 2, 3, 5, 6, 10, 13, 18, 24, 33, 42, 57, 72, 94, 119, 153, 190, 242, 299, 374, 460, 570, 695, 855, 1036, 1262, 1523, 1843, 2210, 2660, 3175, 3797, 4514, 5372, 6357, 7533, 8880, 10474, 12306, 14459, 16925, 19818, 23125, 26981, 31392, 36512, 42355
OFFSET
1,2
COMMENTS
Case k=6,i=5 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ sin(5*Pi/13) * 5^(1/4) * exp(2*Pi*sqrt(5*n/39)) / (3^(1/4) * 13^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 22 2015
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(13*k-1)) * (1 - x^(13*k-2)) * (1 - x^(13*k-3)) * (1 - x^(13*k-4)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-9)) * (1 - x^(13*k-10)) * (1 - x^(13*k-11)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 22 2015 *)
CROSSREFS
Sequence in context: A376807 A018429 A341125 * A195054 A341126 A341127
KEYWORD
nonn,easy
STATUS
approved