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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 00:37 EDT 2020. Contains 337265 sequences. (Running on oeis4.)