A035950 - OEIS

A035950

Number of partitions of n into parts not of the form 13k, 13k+2 or 13k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 5 are greater than 1.

1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 25, 34, 43, 55, 70, 89, 111, 140, 173, 215, 265, 326, 397, 487, 590, 715, 863, 1041, 1247, 1497, 1785, 2129, 2530, 3003, 3551, 4200, 4947, 5823, 6837, 8020, 9380, 10967, 12787, 14898, 17322, 20120, 23322, 27018, 31235

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OFFSET

1,3

COMMENTS

Case k=6,i=2 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..49.

FORMULA

a(n) ~ sin(2*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-3)) * (1 - x^(13*k-4)) * (1 - x^(13*k-5)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-8)) * (1 - x^(13*k-9)) * (1 - x^(13*k-10)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 22 2015 *)

CROSSREFS

Sequence in context: A303944 A039855 A175868 * A175864 A373120 A133153

Adjacent sequences: A035947 A035948 A035949 * A035951 A035952 A035953

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved