A035954 Number of partitions of n into parts not of the form 13k, 13k+6 or 13k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 5 are greater than 1.

1, 1, 2, 3, 5, 7, 10, 13, 19, 25, 34, 44, 59, 75, 98, 124, 159, 199, 252, 312, 391, 481, 595, 727, 893, 1084, 1320, 1594, 1928, 2315, 2784, 3325, 3977, 4730, 5627, 6664, 7894, 9310, 10981, 12905, 15162, 17756, 20787, 24263, 28310, 32946, 38317, 44462

Offset

0,3

Comments

Case k=6,i=6 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ sin(6*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; 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-5)) * (1 - x^(13*k-8)) * (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: A238863 A060688 A005691 * A023192 A064480 A274111

Adjacent sequences: A035951 A035952 A035953 * A035955 A035956 A035957

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Seiichi Manyama, May 08 2018

Status

approved