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A035964
Number of partitions in parts not of the form 17k, 17k+3 or 17k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 7 are greater than 1.
0
1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 78, 98, 128, 159, 204, 252, 319, 392, 490, 599, 742, 902, 1107, 1339, 1632, 1964, 2378, 2849, 3429, 4091, 4897, 5819, 6933, 8207, 9733, 11481, 13562, 15943, 18761, 21985, 25780, 30121, 35204, 41013
OFFSET
1,2
COMMENTS
Case k=8,i=3 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) * sin(3*Pi/17) / (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+ 3-17))*(1 - x^(17*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A326526 A035951 A035957 * A035972 A035981 A035991
KEYWORD
nonn,easy
STATUS
approved