A035970 Number of partitions in parts not of the form 19k, 19k+1 or 19k-1. Also number of partitions with no part of size 1 and differences between parts at distance 8 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 87, 104, 135, 163, 206, 248, 312, 373, 463, 555, 681, 813, 992, 1179, 1428, 1695, 2037, 2411, 2885, 3401, 4048, 4763, 5641, 6617, 7808, 9131, 10733, 12524, 14664, 17067, 19925, 23128, 26917, 31178

Offset

1,4

Comments

Case k=9,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(4*Pi*sqrt(2*n/57)) * 2^(3/4) * sin(Pi/19) / (3^(1/4) * 19^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 1-19))*(1 - x^(19*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A240015 A035962 A240016 * A240017 A035979 A240018

Adjacent sequences: A035967 A035968 A035969 * A035971 A035972 A035973

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved