

A036006


Number of partitions of n into parts not of the form 25k, 25k+7 or 25k7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 11 are greater than 1.


0



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
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OFFSET

1,2


COMMENTS

Case k=12,i=7 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(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+ 725))*(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 A262371 A184642
Adjacent sequences: A036003 A036004 A036005 * A036007 A036008 A036009


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



