

A036010


Number of partitions of n into parts not of the form 25k, 25k+11 or 25k11. Also number of partitions with at most 10 parts of size 1 and differences between parts at distance 11 are greater than 1.


0



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
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OFFSET

1,2


COMMENTS

Case k=12,i=11 of Gordon Theorem.


REFERENCES

G. E. Andrews, The Theory of Partitions, AddisonWesley, 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+1125))*(1  x^(25*k11))/(1  x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)


CROSSREFS

Sequence in context: A008633 A238868 A035999 * A328545 A192061 A218511
Adjacent sequences: A036007 A036008 A036009 * A036011 A036012 A036013


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



