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A035961 Number of partitions of n into parts not of the form 15k, 15k+7 or 15k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 6 are greater than 1. 1
1, 1, 2, 3, 5, 7, 11, 14, 20, 27, 37, 48, 65, 83, 109, 139, 179, 225, 287, 357, 449, 556, 691, 848, 1047, 1276, 1561, 1893, 2299, 2772, 3348, 4015, 4820, 5756, 6874, 8171, 9716, 11501, 13614, 16058, 18932, 22249, 26138, 30613, 35838, 41848, 48831 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Case k=7,i=7 of Gordon Theorem.

REFERENCES

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ exp(2*Pi*sqrt(2*n/15)) * 2^(1/4) * cos(Pi/30) / (15^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

With[ {n=30}, Series[ 1/Product[ (1 - Switch[ Mod[ k, 15 ], 0, 0, 7, 0, 8, 0, _, x^k ]), {k, 1, n} ], {x, 0, n} ] ]

nmax = 60; CoefficientList[Series[Product[(1 - x^(15*k))*(1 - x^(15*k+ 7-15))*(1 - x^(15*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A008629 A238864 A070289 * A051056 A055803 A023027

Adjacent sequences:  A035958 A035959 A035960 * A035962 A035963 A035964

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

a(0)=1 prepended by Seiichi Manyama, May 08 2018

STATUS

approved

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Last modified July 31 02:33 EDT 2021. Contains 346367 sequences. (Running on oeis4.)