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A035957 Number of partitions in parts not of the form 15k, 15k+3 or 15k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 6 are greater than 1. 0
1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 46, 58, 77, 96, 125, 155, 198, 244, 308, 378, 471, 574, 709, 860, 1053, 1270, 1544, 1854, 2239, 2676, 3213, 3824, 4567, 5414, 6435, 7600, 8993, 10584, 12474, 14632, 17180, 20088, 23505, 27403, 31960, 37154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=7,i=3 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..47.

FORMULA

a(n) ~ exp(2*Pi*sqrt(2*n/15)) * sqrt(5 - sqrt(5)) / (2^(5/4) * 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+ 3-15))*(1 - x^(15*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A240308 A326526 A035951 * A035964 A035972 A035981

Adjacent sequences:  A035954 A035955 A035956 * A035958 A035959 A035960

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 20 10:09 EST 2019. Contains 329334 sequences. (Running on oeis4.)