A109705 Number of partitions of n into parts each equal to 3 mod 7.

1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 1, 2, 4, 2, 2, 4, 4, 2, 4, 5, 3, 4, 6, 5, 4, 6, 7, 5, 6, 8, 8, 6, 9, 11, 7, 9, 13, 10, 9, 14, 14, 10, 15, 17, 14, 15, 19, 19, 16, 20, 24, 20, 21, 27, 27, 22, 29, 33, 27, 30, 38, 35, 32, 41, 44, 37, 43, 51, 47, 45

Offset

0,21

Links

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

Formula

G.f.: 1/product(1-x^(3+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006

a(n) ~ Gamma(3/7) * exp(Pi*sqrt(2*n/21)) / (2^(12/7) * 3^(3/14) * 7^(2/7) * Pi^(4/7) * n^(5/7)) * (1 + (23*Pi/(168*sqrt(42)) - 15*sqrt(3/14)/(7*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284444(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 28 2017

Example

a(20)=2 because we have 20=17+3=10+10.

Maple

g:=1/product(1-x^(3+7*j), j=0..20): gser:=series(g, x=0, 90): seq(coeff(gser, x, n), n=0..87); # Emeric Deutsch, Apr 14 2006

Mathematica

nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+3)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)

Crossrefs

Sequence in context: A115268 A103610 A305875 * A352578 A278341 A276520

Adjacent sequences: A109702 A109703 A109704 * A109706 A109707 A109708

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