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%I #22 Mar 18 2020 09:00:56
%S 1,0,0,0,0,1,2,9,49,455,5784,90940,1620491,31478651,656784488,
%T 14621878339,345975756388
%N Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 5.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_ge_g_index">Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g</a>
%F This sequence is the Euler transformation of A014372.
%t A014372 = Cases[Import["https://oeis.org/A014372/b014372.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerTransform is defined in A005195 *)
%t EulerTransform[Rest @ A014372] (* _Jean-François Alcover_, Dec 04 2019, updated Mar 18 2020 *)
%Y 3-regular simple graphs with girth at least 5: A014372 (connected), A185235 (disconnected), this sequence (not necessarily connected).
%Y Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), A185334 (g=4), this sequence (g=5), A185336 (g=6).
%Y Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).
%Y Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), A185305 (triangle); specified degree k: A185325 (k=2), this sequence (k=3).
%K nonn,more,hard
%O 0,7
%A _Jason Kimberley_, Jan 28, 2011