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

0,13

Comments

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

Links

Table of n, a(n) for n=0..67.

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

Formula

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

Prog

(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 */
(Magma) A185225 := func<n|n eq 0 select 0 else #RestrictedPartitions(n, {5..n-1})>;

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).

Sequence in context: A114096 A008582 A069911 * A027196 A325877 A100928

Adjacent sequences: A185222 A185223 A185224 * A185226 A185227 A185228

Keyword

nonn,easy

Author

Jason Kimberley, Feb 22 2011

Extensions

More terms from Joerg Arndt, Jul 26 2011

Status

approved