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A035976 Number of partitions of n into parts not of the form 19k, 19k+7 or 19k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 8 are greater than 1. 0
1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 69, 89, 118, 151, 196, 248, 318, 398, 504, 627, 784, 968, 1201, 1472, 1811, 2207, 2695, 3266, 3964, 4777, 5764, 6916, 8299, 9912, 11840, 14080, 16744, 19837, 23492, 27730, 32717, 38485, 45246, 53055, 62167 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=9,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..46.

FORMULA

a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(5*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+ 7-19))*(1 - x^(19*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A112581 A288255 A325853 * A035985 A035995 A036006

Adjacent sequences:  A035973 A035974 A035975 * A035977 A035978 A035979

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)