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A035993 Number of partitions of n into parts not of the form 23k, 23k+5 or 23k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 10 are greater than 1. 0
1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 79, 105, 134, 175, 220, 283, 354, 449, 558, 700, 863, 1074, 1316, 1622, 1978, 2421, 2934, 3569, 4305, 5204, 6250, 7515, 8984, 10753, 12803, 15252, 18094, 21468, 25373, 29992, 35330, 41610, 48863, 57358 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=11,i=5 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..46.

FORMULA

a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * sin(5*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+ 5-23))*(1 - x^(23*k- 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A035966 A035974 A035983 * A036004 A027339 A039837

Adjacent sequences:  A035990 A035991 A035992 * A035994 A035995 A035996

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 10 04:38 EDT 2020. Contains 336368 sequences. (Running on oeis4.)