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%I #23 Feb 11 2024 22:51:41
%S 0,0,0,1,3,59,7847,3459376,2585136287,2807104844073
%N Number of connected 5-regular (or quintic) simple graphs on 2n vertices with girth exactly 3.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Girth.html">Girth</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuinticGraph.html">Quintic Graph</a>.
%F a(n) = A006821(n) - A058275(n).
%Y Connected k-regular simple graphs with girth exactly 3: A006923 (k=3), A184943 (k=4), this sequence (k=5), A184963 (k=6), A184973 (k=7), A184983 (k=8), A184993 (k=9).
%Y Connected 5-regular simple graphs with girth at least g: A006821 (g=3), A058275 (g=4).
%Y Connected 5-regular simple graphs with girth exactly g: this sequence (g=3), A184954 (g=4), A184955 (g=5).
%K nonn,more,hard
%O 0,5
%A _Jason Kimberley_, Feb 27 2011
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