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A035947 Number of partitions of n into parts not of the form 11k, 11k+4 or 11k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 4 are greater than 1. 0
1, 2, 3, 4, 6, 9, 11, 16, 21, 28, 36, 48, 60, 78, 98, 124, 154, 194, 238, 296, 362, 444, 539, 658, 793, 960, 1152, 1384, 1652, 1976, 2345, 2789, 3299, 3902, 4596, 5416, 6352, 7454, 8715, 10186, 11869, 13828, 16059, 18648, 21598, 25000, 28873, 33332 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=5,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..48.

FORMULA

a(n) ~ cos(3*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-3)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (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: A130899 A007210 A198394 * A338914 A048249 A288734

Adjacent sequences:  A035944 A035945 A035946 * A035948 A035949 A035950

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified January 20 19:22 EST 2021. Contains 340332 sequences. (Running on oeis4.)