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%I #28 May 01 2014 02:39:57
%S 1,0,0,0,0,1,1,7,388,406824,1125022325,3813549359274
%N Number of connected 5-regular simple graphs on 2n vertices with girth at least 4.
%C The null graph on 0 vertices is vacuously connected and 5-regular; since it is acyclic, it has infinite girth. [From _Jason Kimberley_, Jan 30 2011]
%D M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From _Jason Kimberley_, Jan 30 2011]
%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>
%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%F a(n) = A185354(n) - A185254(n);
%F This sequence is the inverse Euler transformation of A185354. - _Jason Kimberley_, Nov 04 2011.
%Y Contribution from _Jason Kimberley_, Jan 30 and Nov 04 2011: (Start)
%Y 5-regular simple graphs on 2n vertices with girth at least 4: this sequence (connected), A185254 (disconnected), A185354 (not necessarily connected).
%Y Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), this sequence (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).
%Y Connected 5-regular simple graphs with girth at least g: A006821 (g=3), this sequence (g=4), A205295 (g=5).
%Y Connected 5-regular simple graphs with girth exactly g: A184953 (g=3), A184954 (g=4), A184955 (g=5). (End)
%K nonn,more,hard
%O 0,8
%A _N. J. A. Sloane_, Dec 17 2000
%E Terms a(10) and a(11) appended, from running Meringer's GENREG for 3.8 and 7886 processor days at U. Ncle., by Jason Kimberley on Jun 28 2010.
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