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A035945 Number of partitions of n into parts not of the form 11k, 11k+2 or 11k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 4 are greater than 1. 0
1, 1, 2, 3, 4, 6, 8, 11, 14, 19, 24, 32, 40, 51, 65, 82, 101, 127, 156, 193, 236, 289, 350, 427, 514, 620, 744, 893, 1064, 1271, 1508, 1790, 2116, 2500, 2942, 3464, 4060, 4758, 5560, 6494, 7560, 8801, 10216, 11852, 13720, 15870, 18317, 21133, 24328 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Case k=5,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..49.

FORMULA

a(n) ~ sin(2*Pi/11) * 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; Rest[CoefficientList[Series[Product[1 / ((1 - x^(11*k-1)) * (1 - x^(11*k-3)) * (1 - x^(11*k-4)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-7)) * (1 - x^(11*k-8)) * (1 - x^(11*k-10)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 21 2015 *)

CROSSREFS

Sequence in context: A003412 A038348 A239467 * A094707 A303663 A117995

Adjacent sequences:  A035942 A035943 A035944 * A035946 A035947 A035948

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified December 5 09:27 EST 2020. Contains 338945 sequences. (Running on oeis4.)