A109704 Number of partitions of n into parts each equal to 2 mod 7.

1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 3, 1, 3, 2, 3, 3, 3, 4, 3, 4, 4, 4, 6, 4, 7, 4, 8, 5, 8, 7, 8, 9, 8, 10, 9, 11, 12, 11, 15, 11, 17, 12, 18, 15, 19, 19, 19, 22, 20, 24, 24, 25, 29, 26, 34, 27, 37, 31, 39, 38, 40, 44, 42, 49, 47, 52, 55, 54, 64, 56, 71, 62, 76, 72, 79

Offset

0,17

Links

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

Formula

G.f.: 1/product(1-x^(2+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006

a(n) ~ Gamma(2/7) * exp(Pi*sqrt(2*n/21)) / (2^(23/14) * 3^(1/7) * 7^(5/14) * Pi^(5/7) * n^(9/14)) * (1 + (11*Pi/(168*sqrt(42)) - 9*sqrt(3/14)/(7*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284443(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 28 2017

Example

a(18)=3 because we have 18=16+2=9+9=2+2+2+2+2+2+2+2+2.

Maple

g:=1/product(1-x^(2+7*j), j=0..20): gser:=series(g, x=0, 87): seq(coeff(gser, x, n), n=0..84); # Emeric Deutsch, Apr 14 2006

Mathematica

nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+2)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)

Crossrefs

Sequence in context: A239930 A226859 A025820 * A073407 A049994 A135732

Adjacent sequences: A109701 A109702 A109703 * A109705 A109706 A109707

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