cp's OEIS Frontend

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

%I A185225 #21 Sep 08 2022 08:45:55
%S A185225 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,
%T A185225 57,69,79,94,109,128,149,175,201,235,271,316,363,422,483,559,642,739,
%U A185225 846,974,1111,1276,1455,1665,1896,2167,2463,2808,3188,3626,4111,4672,5286,5994,6777,7670,8661,9790,11036
%N A185225 Number of disconnected 2-regular simple graphs on n vertices with girth at least 5.
%C A185225 Number of partitions of n with smallest part >= 5 and at least 2 parts.
%H A185225 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/D_k-reg_girth_ge_g_index">Index of sequences counting disconnected k-regular simple graphs with girth at least g</a>
%F A185225 G.f.: -1/(1-q) + Sum_{n>=0} q^n/Product_{k=5..n} (1 - q^k).  [_Joerg Arndt_, Jul 26 2011]
%o A185225 (PARI) N=66;  q='q+O('q^N);
%o A185225 gf= -1/(1-q) + sum(n=0, N, q^n/prod(k=5,n, 1-q^k) ) /* = +q^10 +q^11 +2*q^12 +... */
%o A185225 v=Vec(gf+'a); v[1]=0; v /* _Joerg Arndt_, Jul 26 2011 */
%o A185225 (Magma) A185225 := func<n|n eq 0 select 0 else #RestrictedPartitions(n,{5..n-1})>;
%Y A185225 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).
%K A185225 nonn,easy
%O A185225 0,13
%A A185225 _Jason Kimberley_, Feb 22 2011
%E A185225 More terms from _Joerg Arndt_, Jul 26 2011