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%I #33 Dec 05 2019 04:16:23
%S 1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%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 4.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_4">Connected regular graphs with girth at least 4</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<4 a(n)=0; for n>=4 , a(n)=1.
%F Inverse Euler transformation of A008484.
%F a(n) = A130543(n) + A000007(n). - _Bruno Berselli_, Jan 31 2011
%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.
%t a[n_] := Switch[n, 0, 1, 1|2|3, 0, _, 1];
%t a /@ Range[0, 101] (* _Jean-François Alcover_, Dec 05 2019 *)
%Y 2-regular simple graphs with girth at least 4: this sequence (connected), A185224 (disconnected), A008484 (not necessarily connected).
%Y Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: this sequence (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).
%Y Connected 2-regular simple graphs with girth at least g: A179184 (g=3), this sequence (g=4), A185115 (g=5), A185116 (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 27 2011
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