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.

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.

Links

Table of n, a(n) for n=1..46.

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

Adjacent sequences: A035964 A035965 A035966 * A035968 A035969 A035970

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved