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A035989 Number of partitions in parts not of the form 23k, 23k+1 or 23k-1. Also number of partitions with no part of size 1 and differences between parts at distance 10 are greater than 1. 1
0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 209, 252, 318, 381, 474, 569, 700, 837, 1024, 1219, 1480, 1760, 2120, 2514, 3015, 3561, 4248, 5008, 5944, 6986, 8261, 9680, 11402, 13331, 15641, 18240, 21338, 24817, 28941 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Case k=11,i=1 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..50.

FORMULA

a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * sin(Pi/23) / (3^(1/4) * 23^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+ 1-23))*(1 - x^(23*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A240017 A035979 A240018 * A240019 A036000 A002865

Adjacent sequences:  A035986 A035987 A035988 * A035990 A035991 A035992

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 21 17:26 EDT 2020. Contains 337919 sequences. (Running on oeis4.)