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A035960 Number of partitions of n into parts not of the form 15k, 15k+6 or 15k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 6 are greater than 1. 0
1, 2, 3, 5, 7, 10, 14, 20, 26, 36, 47, 63, 81, 106, 135, 174, 219, 278, 347, 436, 539, 670, 823, 1014, 1237, 1512, 1834, 2227, 2685, 3240, 3887, 4665, 5570, 6650, 7906, 9396, 11124, 13164, 15526, 18302, 21508, 25260, 29587, 34630, 40434, 47174 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=7,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(2*Pi*sqrt(2*n/15)) * (3 + sqrt(5))^(1/4) / (2 * 3^(3/4) * sqrt(5) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(15*k))*(1 - x^(15*k+ 6-15))*(1 - x^(15*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A325858 A237269 A116634 * A288254 A023893 A065094

Adjacent sequences:  A035957 A035958 A035959 * A035961 A035962 A035963

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)