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A035946 Number of partitions in parts not of the form 11k, 11k+3 or 11k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 4 are greater than 1. 0
1, 2, 2, 4, 5, 8, 10, 14, 18, 25, 31, 42, 52, 68, 84, 108, 133, 168, 205, 256, 311, 384, 463, 567, 681, 826, 988, 1190, 1416, 1696, 2009, 2392, 2823, 3344, 3931, 4636, 5431, 6376, 7445, 8708, 10135, 11812, 13706, 15920, 18423, 21332, 24618, 28424 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=5,i=3 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..48.

FORMULA

a(n) ~ cos(5*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; Rest[CoefficientList[Series[Product[1 / ((1 - x^(11*k-1)) * (1 - x^(11*k-2)) * (1 - x^(11*k-4)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-7)) * (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: A308954 A053097 A331443 * A303939 A326446 A323530

Adjacent sequences:  A035943 A035944 A035945 * A035947 A035948 A035949

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.)