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%I #10 Dec 04 2019 21:03:00
%S 1,0,0,0,0,0,0,1,1,5,32,385,7574,181227,4624502,122090545,3328929960,
%T 93990692632,2754222605808
%N Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 6.
%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_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 A014374.
%t A014374 = Cases[Import["https://oeis.org/A014374/b014374.txt", "Table"], {_, _}][[All, 2]];
%t etr[f_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d f[d], {d, Divisors[j]}] b[n - j], {j, 1, n}]/n]; b];
%t a = etr[A014374[[# + 1]]&];
%t a /@ Range[0, Length[A014374] - 1] (* _Jean-François Alcover_, Dec 04 2019 *)
%Y 3-regular simple graphs with girth at least 6: A014374 (connected), A185236 (disconnected), this sequence (not necessarily connected).
%Y Not necessarily connected k-regular simple graphs with girth at least 6: A185326 (k=2), this sequence (k=3).
%Y Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), A185334 (g=4), A185335 (g=5), this sequence (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 0,10
%A _Jason Kimberley_, Jan 28 2012
%E a(18) from A014374 from _Jean-François Alcover_, Dec 04 2019
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