A035949 Number of partitions in parts not of the form 13k, 13k+1 or 13k-1. Also number of partitions with no part of size 1 and differences between parts at distance 5 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 20, 23, 32, 39, 51, 61, 80, 95, 122, 146, 183, 219, 273, 324, 399, 475, 578, 685, 830, 979, 1177, 1387, 1655, 1945, 2311, 2705, 3198, 3737, 4396, 5121, 6003, 6973, 8143, 9439, 10981, 12697, 14730, 16987, 19648, 22614

Offset

1,4

Comments

Case k=6,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) ~ sin(Pi/13) * 5^(1/4) * exp(2*Pi*sqrt(5*n/39)) / (3^(1/4) * 13^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 22 2015

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(13*k-2)) * (1 - x^(13*k-3)) * (1 - x^(13*k-4)) * (1 - x^(13*k-5)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-8)) * (1 - x^(13*k-9)) * (1 - x^(13*k-10)) * (1 - x^(13*k-11)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 22 2015 *)

Crossrefs

Sequence in context: A266778 A107235 A266779 * A347445 A240014 A266780

Adjacent sequences: A035946 A035947 A035948 * A035950 A035951 A035952

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved