A036001 Number of partitions of n into parts not of the form 25k, 25k+2 or 25k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 11 are greater than 1.

1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 75, 96, 121, 154, 193, 242, 302, 375, 462, 572, 701, 858, 1047, 1275, 1545, 1872, 2257, 2718, 3264, 3912, 4674, 5581, 6641, 7892, 9359, 11082, 13090, 15447, 18186, 21385, 25102, 29425, 34430, 40247

Offset

1,3

Comments

Case k=12,i=2 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) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * sin(2*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+ 2-25))*(1 - x^(25*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035971 A035980 A035990 * A027336 A237830 A023434

Adjacent sequences: A035998 A035999 A036000 * A036002 A036003 A036004

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved