A036002 Number of partitions in parts not of the form 25k, 25k+3 or 25k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 79, 99, 130, 162, 209, 259, 330, 407, 511, 627, 781, 953, 1176, 1428, 1749, 2114, 2572, 3095, 3743, 4485, 5394, 6438, 7706, 9162, 10916, 12933, 15346, 18120, 21418, 25208, 29691, 34840, 40898, 47852

Offset

1,2

Comments

Case k=12,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..47.

Formula

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

Crossrefs

Sequence in context: A035972 A035981 A035991 * A104504 A027337 A364892

Adjacent sequences: A035999 A036000 A036001 * A036003 A036004 A036005

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved