A036006 Number of partitions of n into parts not of the form 25k, 25k+7 or 25k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 70, 90, 120, 154, 201, 255, 328, 412, 524, 654, 821, 1017, 1267, 1558, 1924, 2353, 2884, 3507, 4272, 5166, 6256, 7531, 9069, 10868, 13027, 15543, 18546, 22045, 26194, 31020, 36719, 43331, 51109, 60120

Offset

1,2

Comments

Case k=12,i=7 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(11*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+ 7-25))*(1 - x^(25*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035976 A035985 A035995 * A027341 A363230 A262371

Adjacent sequences: A036003 A036004 A036005 * A036007 A036008 A036009

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved