A109700 Number of partitions of n into parts each equal to 4 mod 5.

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 3, 4, 2, 2, 3, 5, 4, 3, 3, 6, 6, 6, 4, 6, 7, 9, 7, 7, 8, 11, 11, 11, 9, 12, 14, 16, 13, 14, 16, 21, 20, 19, 18, 24, 26, 27, 24, 27, 31, 36, 34, 34, 35, 43, 45, 47, 43, 49, 55, 62, 58, 59, 63, 75, 77, 77, 75, 87

Offset

0,19

Links

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

Formula

G.f.: 1/product(1-x^(4+5j), j=0..infinity). - Emeric Deutsch, Mar 30 2006

a(n) ~ Gamma(4/5) * exp(Pi*sqrt(2*n/15)) / (2^(19/10) * 3^(2/5) * 5^(1/10) * Pi^(1/5) * n^(9/10)) * (1 - (9*sqrt(6/5)/(5*Pi) + Pi/(120*sqrt(30))) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284103(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 20 2017

Example

a(30)=2 since 30 = 14+4+4+4+4 = 9+9+4+4+4

Maple

g:=1/product(1-x^(4+5*j), j=0..25): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=0..90); # Emeric Deutsch, Mar 30 2006

Mathematica

nmax=100; CoefficientList[Series[Product[1/(1-x^(5*k+4)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)

Crossrefs

Cf. A284103.

Cf. similar sequences of number of partitions of n into parts congruent to m-1 mod m: A000009 (m=2), A035386 (m=3), A035462 (m=4), this sequence (m=5), A109702 (m=6), A109708 (m=7).

Sequence in context: A353362 A256122 A087048 * A087742 A340996 A072530

Adjacent sequences: A109697 A109698 A109699 * A109701 A109702 A109703

Keyword

nonn

Author

Erich Friedman, Aug 07 2005

Extensions

More terms from Michael Somos, Aug 10 2005

Status

approved