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A035969
Number of partitions of n into parts not of the form 17k, 17k+8 or 17k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 7 are greater than 1.
2
1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 39, 51, 69, 89, 117, 150, 194, 245, 313, 392, 494, 614, 766, 944, 1168, 1430, 1754, 2135, 2601, 3146, 3810, 4585, 5519, 6611, 7917, 9440, 11253, 13361, 15856, 18755, 22169, 26124, 30766, 36132, 42401, 49639, 58063
OFFSET
0,3
COMMENTS
Case k=8,i=8 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
LINKS
FORMULA
a(n) ~ exp(2*Pi*sqrt(7*n/51)) * 7^(1/4) * cos(Pi/34) / (3^(1/4) * 17^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 8-17))*(1 - x^(17*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A347573 A238865 A326978 * A355027 A332745 A042953
KEYWORD
nonn,easy
EXTENSIONS
a(0)=1 prepended by Seiichi Manyama, May 08 2018
STATUS
approved