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A036001 Number of partitions of n into parts not of the form 25k, 25k+2 or 25k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 11 are greater than 1. 0
1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 75, 96, 121, 154, 193, 242, 302, 375, 462, 572, 701, 858, 1047, 1275, 1545, 1872, 2257, 2718, 3264, 3912, 4674, 5581, 6641, 7892, 9359, 11082, 13090, 15447, 18186, 21385, 25102, 29425, 34430, 40247 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Case k=12,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..48.

FORMULA

a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * sin(2*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+ 2-25))*(1 - x^(25*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A035971 A035980 A035990 * A027336 A237830 A023434

Adjacent sequences:  A035998 A035999 A036000 * A036002 A036003 A036004

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)