A185225 Number of disconnected 2-regular simple graphs on n vertices with girth at least 5.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 14, 17, 20, 25, 29, 35, 41, 49, 57, 69, 79, 94, 109, 128, 149, 175, 201, 235, 271, 316, 363, 422, 483, 559, 642, 739, 846, 974, 1111, 1276, 1455, 1665, 1896, 2167, 2463, 2808, 3188, 3626, 4111, 4672, 5286, 5994, 6777, 7670, 8661, 9790, 11036

Offset: 0

Author

Jason Kimberley, Feb 22 2011

Keywords

• nonn
• easy

Comments

Number of partitions of n with smallest part >= 5 and at least 2 parts.

Links

• Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Crossrefs

Disconnected 2-regular simple graphs with girth at least g: A165652 (g=3), A185224 (g=4), this sequence (g=5), A185226 (g=6), A185227 (g=7), A185228 (g=8), A185229 (g=9).

Programs

Magma

A185225 := func;

PARI

N=66;  q='q+O('q^N);
gf= -1/(1-q) + sum(n=0, N, q^n/prod(k=5,n, 1-q^k) ) /* = +q^10 +q^11 +2*q^12 +... */
v=Vec(gf+'a); v[1]=0; v /* Joerg Arndt, Jul 26 2011 */

Formula

G.f.: -1/(1-q) + Sum_{n>=0} q^n/Product_{k=5..n} (1 - q^k). [Joerg Arndt, Jul 26 2011]

Extensions

More terms from Joerg Arndt, Jul 26 2011