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A035955 Number of partitions in parts not of the form 15k, 15k+1 or 15k-1. Also number of partitions with no part of size 1 and differences between parts at distance 6 are greater than 1. 0
0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 33, 40, 53, 64, 84, 100, 129, 155, 195, 234, 293, 349, 431, 515, 629, 748, 909, 1076, 1298, 1535, 1837, 2166, 2582, 3032, 3595, 4214, 4972, 5810, 6831, 7959, 9321, 10837, 12643, 14662, 17057, 19728, 22880, 26409 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Case k=7,i=1 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..51.

FORMULA

a(n) ~ exp(2*Pi*sqrt(2*n/15)) * 2^(1/4) * sin(Pi/15) / (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+ 1-15))*(1 - x^(15*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A240014 A266780 A266781 * A240015 A035962 A240016

Adjacent sequences:  A035952 A035953 A035954 * A035956 A035957 A035958

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 26 18:29 EST 2020. Contains 332293 sequences. (Running on oeis4.)