A035952 - OEIS

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A035952

Number of partitions of n into parts not of the form 13k, 13k+4 or 13k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 5 are greater than 1.

1, 2, 3, 4, 6, 9, 12, 17, 22, 30, 39, 52, 66, 86, 109, 139, 174, 220, 272, 340, 419, 517, 632, 775, 940, 1144, 1381, 1668, 2002, 2406, 2873, 3433, 4082, 4852, 5745, 6801, 8018, 9452, 11105, 13039, 15266, 17864, 20845, 24310, 28284, 32881, 38145

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OFFSET

1,2

COMMENTS

Case k=6,i=4 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) ~ sin(4*Pi/13) * 5^(1/4) * exp(2*Pi*sqrt(5*n/39)) / (3^(1/4) * 13^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 22 2015

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(13*k-1)) * (1 - x^(13*k-2)) * (1 - x^(13*k-3)) * (1 - x^(13*k-5)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-8)) * (1 - x^(13*k-10)) * (1 - x^(13*k-11)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 22 2015 *)

CROSSREFS

Sequence in context: A350842 A018550 A248475 * A335754 A105781 A035958

Adjacent sequences: A035949 A035950 A035951 * A035953 A035954 A035955

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved