A035962 Number of partitions in parts not of the form 17k, 17k+1 or 17k-1. Also number of partitions with no part of size 1 and differences between parts at distance 7 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 54, 65, 86, 103, 133, 160, 202, 243, 305, 364, 451, 540, 661, 788, 960, 1139, 1377, 1632, 1958, 2314, 2764, 3253, 3866, 4542, 5370, 6289, 7410, 8652, 10154, 11830, 13830, 16072, 18735, 21714, 25234, 29185

Offset

1,4

Comments

Case k=8,i=1 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..51.

Formula

a(n) ~ exp(2*Pi*sqrt(7*n/51)) * 7^(1/4) * sin(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+ 1-17))*(1 - x^(17*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A266781 A035955 A240015 * A240016 A035970 A240017

Adjacent sequences: A035959 A035960 A035961 * A035963 A035964 A035965

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved