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A035968
Number of partitions of n into parts not of the form 17k, 17k+7 or 17k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 7 are greater than 1.
0
1, 2, 3, 5, 7, 11, 14, 21, 28, 38, 50, 68, 87, 115, 147, 190, 240, 307, 383, 484, 601, 749, 923, 1143, 1397, 1715, 2086, 2541, 3073, 3722, 4476, 5390, 6454, 7728, 9212, 10983, 13035, 15471, 18295, 21624, 25478, 30005, 35229, 41344, 48393, 56602
OFFSET
1,2
COMMENTS
Case k=8,i=7 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ exp(2*Pi*sqrt(7*n/51)) * 7^(1/4) * cos(3*Pi/34) / (3^(1/4) * 17^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 7-17))*(1 - x^(17*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A055803 A023027 A051014 * A112581 A288255 A325853
KEYWORD
nonn,easy
STATUS
approved