A035951 Number of partitions in parts not of the form 13k, 13k+3 or 13k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 5 are greater than 1.

1, 2, 2, 4, 5, 8, 10, 15, 19, 26, 33, 45, 56, 74, 92, 119, 147, 187, 230, 289, 353, 438, 532, 655, 791, 965, 1160, 1405, 1681, 2023, 2409, 2883, 3420, 4070, 4809, 5698, 6707, 7911, 9281, 10904, 12750, 14925, 17397, 20296, 23590, 27431, 31795, 36864

Offset

1,2

Comments

Case k=6,i=3 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..48.

Formula

a(n) ~ sin(3*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-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-11)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 22 2015 *)

Crossrefs

Sequence in context: A131945 A240308 A326526 * A035957 A035964 A035972

Adjacent sequences: A035948 A035949 A035950 * A035952 A035953 A035954

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved