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A109707 Number of partitions of n into parts each equal to 5 mod 7. 4
1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 1, 1, 0, 2, 1, 2, 1, 1, 2, 1, 3, 1, 3, 2, 2, 3, 1, 4, 2, 4, 3, 2, 5, 2, 6, 3, 5, 5, 3, 7, 3, 8, 5, 6, 8, 4, 10, 5, 10, 8, 8, 11, 6, 13, 8, 13, 12, 10, 15, 9, 18, 12, 17, 16, 14, 21, 13, 23, 17, 22, 23, 18, 28, 18, 31, 24, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,25

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.

FORMULA

G.f.: 1/product(1-x^(5+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006

a(n) ~ Gamma(5/7) * exp(Pi*sqrt(2*n/21)) / (2^(13/7) * 3^(5/14) * 7^(1/7) * Pi^(2/7) * n^(6/7)) * (1 + (11*Pi/(168*sqrt(42)) - 15*sqrt(6/7)/(7*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284446(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 28 2017

EXAMPLE

a(36)=3 because we have 36=26+5+5=19+12+5=12+12+12.

MAPLE

g:=1/product(1-x^(5+7*j), j=0..20): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=0..92); # Emeric Deutsch, Apr 14 2006

MATHEMATICA

nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+5)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)

CROSSREFS

Sequence in context: A277045 A146061 A135936 * A214578 A064272 A117479

Adjacent sequences:  A109704 A109705 A109706 * A109708 A109709 A109710

KEYWORD

nonn

AUTHOR

Erich Friedman, Aug 07 2005

EXTENSIONS

Changed offset to 0 and added a(0)=1 by Vaclav Kotesovec, Feb 27 2015

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)