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A035995 Number of partitions of n into parts not of the form 23k, 23k+7 or 23k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 10 are greater than 1. 0
1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 70, 90, 120, 154, 200, 254, 327, 410, 521, 650, 815, 1009, 1256, 1543, 1904, 2327, 2849, 3462, 4214, 5091, 6160, 7410, 8915, 10675, 12785, 15242, 18172, 21583, 25623, 30320, 35862, 42285, 49835, 58576 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=11,i=7 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(9*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+ 7-23))*(1 - x^(23*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A325853 A035976 A035985 * A036006 A027341 A262371

Adjacent sequences:  A035992 A035993 A035994 * A035996 A035997 A035998

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 4 19:44 EDT 2020. Contains 336202 sequences. (Running on oeis4.)