A035955 Number of partitions in parts not of the form 15k, 15k+1 or 15k-1. Also number of partitions with no part of size 1 and differences between parts at distance 6 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 33, 40, 53, 64, 84, 100, 129, 155, 195, 234, 293, 349, 431, 515, 629, 748, 909, 1076, 1298, 1535, 1837, 2166, 2582, 3032, 3595, 4214, 4972, 5810, 6831, 7959, 9321, 10837, 12643, 14662, 17057, 19728, 22880, 26409

Offset

1,4

Comments

Case k=7,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(2*n/15)) * 2^(1/4) * sin(Pi/15) / (15^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(15*k))*(1 - x^(15*k+ 1-15))*(1 - x^(15*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A240014 A266780 A266781 * A240015 A035962 A240016

Adjacent sequences: A035952 A035953 A035954 * A035956 A035957 A035958

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved