A036010 Number of partitions of n into parts not of the form 25k, 25k+11 or 25k-11. Also number of partitions with at most 10 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 76, 99, 131, 170, 222, 283, 365, 461, 586, 735, 924, 1148, 1432, 1767, 2183, 2678, 3286, 4004, 4883, 5918, 7172, 8651, 10428, 12516, 15017, 17946, 21430, 25509, 30337, 35969, 42614, 50347, 59428, 69982

Offset

1,2

Comments

Case k=12,i=11 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(3*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+11-25))*(1 - x^(25*k-11))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A347576 A238868 A035999 * A328545 A192061 A218511

Adjacent sequences: A036007 A036008 A036009 * A036011 A036012 A036013

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved