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%I #21 Aug 29 2014 11:01:24
%S 1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N Number of connected 2-regular simple graphs on n vertices with girth at least 6.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_6">Connected regular graphs with girth at least 6</a>
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_ge_g_index">Index of sequences counting connected k-regular simple graphs with girth at least g</a>
%F a(0)=1; for 0<n<6 a(n)=0; for n>=6 , a(n)=1.
%F This sequence is the inverse Euler transformation of A185326.
%e The null graph is vacuously 2-regular and, being acyclic, has infinite girth.
%e There are no 2-regular simple graphs with 1 or 2 vertices.
%e The n-cycle has girth n.
%Y 2-regular simple graphs with girth at least 6: this sequence (connected), A185226 (disconnected), A185326 (not necessarily connected).
%Y Connected k-regular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: this sequence (k=2), A014374 (k=3), A058348 (k=4).
%Y Connected 2-regular simple graphs with girth at least g: A179184 (g=3), A185114 (g=4), A185115 (g=5), this sequence (g=6), A185117 (g=7), A185118 (g=8), A185119 (g=9).
%Y Connected 2-regular simple graphs with girth exactly g: A185013 (g=3), A185014 (g=4), A185015 (g=5), A185016 (g=6), A185017 (g=7), A185018 (g=8).
%K nonn,easy
%O 0
%A _Jason Kimberley_, Jan 28 2011
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