A036003 Number of partitions of n into parts not of the form 25k, 25k+4 or 25k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 41, 55, 71, 93, 120, 154, 196, 250, 314, 396, 494, 616, 763, 945, 1161, 1427, 1744, 2128, 2585, 3138, 3790, 4575, 5502, 6606, 7908, 9455, 11268, 13415, 15928, 18886, 22341, 26397, 31116, 36638, 43053, 50527, 59192

Offset

1,2

Comments

Case k=12,i=4 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) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * sin(4*Pi/25) / (3^(1/4) * 5^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 4-25))*(1 - x^(25*k- 4))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035973 A035982 A035992 * A027338 A064174 A062121

Adjacent sequences: A036000 A036001 A036002 * A036004 A036005 A036006

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved