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A035975 Number of partitions of n into parts not of the form 19k, 19k+6 or 19k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 8 are greater than 1. 0
1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 85, 112, 144, 186, 236, 301, 378, 477, 594, 741, 916, 1134, 1391, 1708, 2083, 2540, 3079, 3732, 4500, 5424, 6508, 7803, 9321, 11125, 13231, 15723, 18628, 22048, 26024, 30688, 36097, 42419, 49736, 58254 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=9,i=6 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(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(7*Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 6-19))*(1 - x^(19*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A035967 A097797 A219601 * A035984 A035994 A036005

Adjacent sequences:  A035972 A035973 A035974 * A035976 A035977 A035978

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 12 05:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)