A036007 Number of partitions of n into parts not of the form 25k, 25k+8 or 25k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 72, 94, 124, 161, 209, 266, 342, 432, 547, 686, 860, 1068, 1329, 1639, 2021, 2478, 3035, 3696, 4501, 5452, 6598, 7954, 9577, 11488, 13769, 16445, 19619, 23341, 27734, 32866, 38907, 45944, 54191, 63784

Offset

1,2

Comments

Case k=12,i=8 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..45.

Formula

a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * cos(9*Pi/50) / (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+ 8-25))*(1 - x^(25*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035986 A035996 A261775 * A027342 A363231 A184643

Adjacent sequences: A036004 A036005 A036006 * A036008 A036009 A036010

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved