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A035943 Number of partitions of n into parts not of the form 9k, 9k+4 or 9k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 3 are greater than 1. 2
1, 1, 2, 3, 4, 5, 8, 10, 14, 18, 24, 30, 40, 49, 63, 78, 98, 120, 150, 182, 224, 271, 330, 396, 480, 572, 687, 817, 974, 1151, 1367, 1608, 1898, 2226, 2614, 3053, 3573, 4157, 4844, 5620, 6524, 7544, 8731, 10066, 11611, 13353, 15356, 17612, 20203, 23112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Case k=4,i=4 of Gordon Theorem.

REFERENCES

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ cos(Pi/18) * exp(2*Pi*sqrt(n)/3) / (3*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Nov 12 2015

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[1 / ((1 - x^(9*k-1)) * (1 - x^(9*k-2)) * (1 - x^(9*k-3)) * (1 - x^(9*k-6)) * (1 - x^(9*k-7)) * (1 - x^(9*k-8)) ), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 12 2015 *)

CROSSREFS

Sequence in context: A238479 A035562 A107234 * A240177 A035555 A039875

Adjacent sequences:  A035940 A035941 A035942 * A035944 A035945 A035946

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

a(0)=1 prepended by Seiichi Manyama, May 08 2018

STATUS

approved

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Last modified October 30 10:25 EDT 2020. Contains 338078 sequences. (Running on oeis4.)