A109707 Number of partitions of n into parts each equal to 5 mod 7.

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

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: A146061 A331186 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