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A035967
Number of partitions of n into parts not of the form 17k, 17k+6 or 17k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 7 are greater than 1.
0
1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 48, 65, 84, 110, 141, 182, 230, 293, 367, 462, 574, 715, 881, 1089, 1333, 1633, 1987, 2419, 2926, 3540, 4259, 5124, 6136, 7344, 8754, 10430, 12381, 14686, 17367, 20520, 24175, 28459, 33415, 39200, 45881, 53649
OFFSET
1,2
COMMENTS
Case k=8,i=6 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(5*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+ 6-17))*(1 - x^(17*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A094023 A123630 A326977 * A097797 A219601 A035975
KEYWORD
nonn,easy
STATUS
approved