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A036003 Number of partitions of n into parts not of the form 25k, 25k+4 or 25k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 11 are greater than 1. 0
1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 41, 55, 71, 93, 120, 154, 196, 250, 314, 396, 494, 616, 763, 945, 1161, 1427, 1744, 2128, 2585, 3138, 3790, 4575, 5502, 6606, 7908, 9455, 11268, 13415, 15928, 18886, 22341, 26397, 31116, 36638, 43053, 50527, 59192 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=12,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) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * sin(4*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+ 4-25))*(1 - x^(25*k- 4))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A035973 A035982 A035992 * A027338 A064174 A062121

Adjacent sequences:  A036000 A036001 A036002 * A036004 A036005 A036006

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified June 6 04:15 EDT 2020. Contains 334859 sequences. (Running on oeis4.)