

A035958


Number of partitions of n into parts not of the form 15k, 15k+4 or 15k4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 6 are greater than 1.


0



1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 40, 54, 69, 90, 115, 147, 185, 235, 292, 366, 453, 561, 689, 848, 1033, 1261, 1529, 1853, 2233, 2693, 3227, 3869, 4618, 5507, 6543, 7771, 9194, 10872, 12817, 15096, 17732, 20814, 24365, 28501, 33265, 38786, 45133
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OFFSET

1,2


COMMENTS

Case k=7,i=4 of Gordon Theorem.


REFERENCES

G. E. Andrews, The Theory of Partitions, AddisonWesley, 1976, p. 109.


LINKS

Table of n, a(n) for n=1..47.


FORMULA

a(n) ~ exp(2*Pi*sqrt(2*n/15)) * 2^(1/4) * cos(7*Pi/30) / (15^(3/4) * n^(3/4)).  Vaclav Kotesovec, May 10 2018


MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1  x^(15*k))*(1  x^(15*k+ 415))*(1  x^(15*k 4))/(1  x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)


CROSSREFS

Sequence in context: A035952 A335754 A105781 * A035965 A035973 A035982
Adjacent sequences: A035955 A035956 A035957 * A035959 A035960 A035961


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



