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A035948 Number of partitions of n into parts not of the form 11k, 11k+5 or 11k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 4 are greater than 1. 2
1, 1, 2, 3, 5, 6, 9, 12, 17, 22, 30, 38, 51, 64, 83, 104, 133, 164, 207, 254, 316, 386, 475, 576, 704, 848, 1027, 1232, 1483, 1768, 2116, 2512, 2989, 3534, 4184, 4926, 5808, 6812, 7996, 9348, 10932, 12735, 14842, 17238, 20022, 23188, 26850, 31008, 35805 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Case k=5,i=5 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/22) * sqrt(2) * exp(4*Pi*sqrt(n/33)) / (3^(1/4) * 11^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 21 2015

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[1 / ((1 - x^(11*k-1)) * (1 - x^(11*k-2)) * (1 - x^(11*k-3)) * (1 - x^(11*k-4)) * (1 - x^(11*k-7)) * (1 - x^(11*k-8)) * (1 - x^(11*k-9)) * (1 - x^(11*k-10)) ), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 21 2015 *)

CROSSREFS

Sequence in context: A046966 A225973 A292444 * A258939 A244747 A241742

Adjacent sequences:  A035945 A035946 A035947 * A035949 A035950 A035951

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 June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)