A035979 Number of partitions in parts not of the form 21k, 21k+1 or 21k-1. Also number of partitions with no part of size 1 and differences between parts at distance 9 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 136, 164, 208, 251, 316, 378, 470, 564, 693, 828, 1012, 1204, 1460, 1735, 2088, 2474, 2964, 3498, 4169, 4911, 5823, 6838, 8079, 9459, 11131, 13003, 15243, 17761, 20759, 24123, 28107

Offset

1,4

Comments

Case k=10,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..50.

Formula

a(n) ~ exp(2*Pi*sqrt(n/7)) * sin(Pi/21) / (sqrt(3) * 7^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+ 1-21))*(1 - x^(21*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A240016 A035970 A240017 * A240018 A035989 A240019

Adjacent sequences: A035976 A035977 A035978 * A035980 A035981 A035982

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved