A035957 - OEIS

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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.

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

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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