A036000 - OEIS

A036000

Number of partitions in parts not of the form 25k, 25k+1 or 25k-1. Also number of partitions with no part of size 1 and differences between parts at distance 11 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 210, 253, 319, 382, 476, 572, 704, 842, 1031, 1228, 1492, 1775, 2140, 2539, 3047, 3601, 4299, 5071, 6023, 7083, 8382, 9828, 11584, 13552, 15912, 18568, 21736, 25296, 29520

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OFFSET

1,4

COMMENTS

Case k=12,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..50.

FORMULA

a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * sin(Pi/25) / (3^(1/4) * 5^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 1-25))*(1 - x^(25*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A240018 A035989 A240019 * A002865 A085811 A187219

Adjacent sequences: A035997 A035998 A035999 * A036001 A036002 A036003

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved