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A035998 Number of partitions of n into parts not of the form 23k, 23k+10 or 23k-10. Also number of partitions with at most 9 parts of size 1 and differences between parts at distance 10 are greater than 1. 0
1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 75, 97, 129, 167, 217, 277, 356, 449, 570, 714, 895, 1112, 1384, 1705, 2104, 2578, 3157, 3844, 4680, 5665, 6857, 8261, 9943, 11923, 14286, 17052, 20339, 24184, 28724, 34023, 40260, 47515, 56024, 65904 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=11,i=10 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..45.

FORMULA

a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * cos(3*Pi/46) / (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+10-23))*(1 - x^(23*k-10))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A246580 A212187 A332280 * A137792 A039905 A036009

Adjacent sequences:  A035995 A035996 A035997 * A035999 A036000 A036001

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified September 18 06:40 EDT 2020. Contains 337166 sequences. (Running on oeis4.)