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%I #32 Mar 18 2020 09:00:51
%S 1,0,0,1,2,6,23,112,801,7840,97723,1436873,23791155,432878091,
%T 8544173926,181519645163,4127569521160
%N Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 4.
%C The null graph on 0 vertices is vacuously 3-regular; since it is acyclic, it has infinite girth.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_girth_ge_4">Not necessarily connected k-regular graphs with girth at least 4</a>
%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 Euler transformation of A014371.
%t A014371 = Cases[Import["https://oeis.org/A014371/b014371.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerTransform is defined in A005195 *)
%t EulerTransform[Rest @ A014371] (* _Jean-François Alcover_, Dec 04 2019, updated Mar 18 2020 *)
%Y 3-regular simple graphs with girth at least 4: A014371 (connected), A185234 (disconnected), this sequence (not necessarily connected).
%Y Not necessarily connected k-regular simple graphs with girth at least 4: A185314 (any k), A185304 (triangle); specified degree k: A008484 (k=2), this sequence (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).
%Y Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), this sequence (g=4), A185335 (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).
%K nonn,more,hard
%O 0,5
%A _Jason Kimberley_, Feb 15 2011
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