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A035992 Number of partitions of n into parts not of the form 23k, 23k+4 or 23k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 10 are greater than 1. 0
1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 41, 55, 71, 93, 120, 154, 196, 250, 313, 395, 493, 614, 760, 941, 1155, 1419, 1733, 2113, 2565, 3112, 3756, 4531, 5445, 6533, 7815, 9338, 11120, 13230, 15697, 18599, 21986, 25960, 30578, 35980, 42250, 49550, 58006 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=11,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..47.

FORMULA

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

CROSSREFS

Sequence in context: A035965 A035973 A035982 * A036003 A027338 A064174

Adjacent sequences:  A035989 A035990 A035991 * A035993 A035994 A035995

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified June 6 11:14 EDT 2020. Contains 334827 sequences. (Running on oeis4.)