A109698 Number of partitions of n into parts each congruent to 2 mod 5.

1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 3, 2, 3, 3, 3, 4, 4, 4, 6, 4, 7, 5, 8, 7, 8, 9, 9, 10, 12, 11, 15, 12, 17, 15, 18, 19, 20, 22, 24, 24, 29, 26, 34, 31, 37, 38, 40, 44, 46, 49, 55, 53, 64, 60, 71, 71, 77, 83, 86, 93, 100, 101, 116, 112, 130, 129, 142, 149, 156, 168, 177

Offset: 0

Author

Erich Friedman, Aug 07 2005

Keywords

• nonn

Examples

			a(12)=2 since 12 = 12 = 2+2+2+2+2+2.
		

Links

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

Crossrefs

Cf. A284280.

Programs

Maple

g:=1/product(1-x^(2+5*i),i=0..20): gser:=series(g,x=0,86): seq(coeff(gser,x,n),n=0..82); # Emeric Deutsch, Feb 15 2006

Mathematica

nmax=100; CoefficientList[Series[Product[1/(1-x^(5*k+2)),{k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)

PARI

Vec(prod(k=0, 100, 1/(1 - x^(5*k + 2))) + O(x^111)) \\ Indranil Ghosh, Mar 24 2017

Formula

G.f.: 1/Product_{j>=0} (1 - x^(2+5j)). - Emeric Deutsch, Feb 15 2006

a(n) ~ Gamma(2/5) * exp(Pi*sqrt(2*n/15)) / (2^(17/10) * 3^(1/5) * 5^(3/10)*Pi^(3/5) * n^(7/10)) * (1 + (11*Pi/(120*sqrt(30)) - 7*sqrt(3/10)/(5*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284280(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 24 2017

Extensions

More terms from Emeric Deutsch, Feb 15 2006