%I #24 May 01 2014 02:37:02

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,15,35,247,1692,17409,197924,

%T 2492824,33117880,461597957,6709514218,101153412903,1597440868898

%N Number of disconnected 4-regular simple graphs on n vertices with girth at least 4.

%H 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 a(n) = A185344(n) - A033886(n) = Euler_transformation(A033886)(n) - A033886(n).

%F a(n) = A185044(n) + A185245(n).

%Y 4-regular simple graphs with girth at least 4: A033886 (connected), this sequence (disconnected), A185344 (not necessarily connected).

%Y Disconnected 4-regular simple graphs with girth at least g: A033483 (g=3), this sequence (g=4), A185245 (g=5), A185246 (g=6).

%Y Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), this sequence (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).

%K nonn,more,hard

%O 0,19

%A _Jason Kimberley_, Feb 22 2011

%E a(31) appended by the author once A033886(23) was known, Nov 03 2011

%E a(31) corrected by the author, Jan 05 2013