A035953 Number of partitions of n into parts not of the form 13k, 13k+5 or 13k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 5 are greater than 1.

1, 2, 3, 5, 6, 10, 13, 18, 24, 33, 42, 57, 72, 94, 119, 153, 190, 242, 299, 374, 460, 570, 695, 855, 1036, 1262, 1523, 1843, 2210, 2660, 3175, 3797, 4514, 5372, 6357, 7533, 8880, 10474, 12306, 14459, 16925, 19818, 23125, 26981, 31392, 36512, 42355

Offset

1,2

Comments

Case k=6,i=5 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..47.

Formula

a(n) ~ sin(5*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-1)) * (1 - x^(13*k-2)) * (1 - x^(13*k-3)) * (1 - x^(13*k-4)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-9)) * (1 - x^(13*k-10)) * (1 - x^(13*k-11)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 22 2015 *)

Crossrefs

Sequence in context: A013931 A018429 A341125 * A195054 A341126 A341127

Adjacent sequences: A035950 A035951 A035952 * A035954 A035955 A035956

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved