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A109700 Number of partitions of n into parts each equal to 4 mod 5. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A069010 A256122 A087048 * A087742 A072530 A184341

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

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Last modified April 23 11:43 EDT 2017. Contains 285322 sequences.