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%I #25 Mar 11 2014 20:28:27
%S 1,0,0,0,0,0,0,1,1,8,741,2887493
%N Number of connected 7-regular simple graphs on 2n vertices with girth at least 4.
%C a(10) was computed by the author in 3 hours using GENREG on Dec 02 2009.
%C a(11) was computed by the author using GENREG over 45.7 processor days at U. Newcastle from Jan 25 to 27 2011.
%D M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.
%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>
%e The a(0)=1 null graph is vacuously 7-regular and connected; since it is acyclic then it has infinite girth.
%e The a(7)=1 graph is the complete bipartite graph K_{7,7} on 14 vertices.
%e The a(8)=1 graph has girth 4, automorphism group of order 80640, and the following adjacency lists:
%e 01 : 02 03 04 05 06 07 08
%e 02 : 01 09 10 11 12 13 14
%e 03 : 01 09 10 11 12 13 15
%e 04 : 01 09 10 11 12 14 15
%e 05 : 01 09 10 11 13 14 15
%e 06 : 01 09 10 12 13 14 15
%e 07 : 01 09 11 12 13 14 15
%e 08 : 01 10 11 12 13 14 15
%e 09 : 02 03 04 05 06 07 16
%e 10 : 02 03 04 05 06 08 16
%e 11 : 02 03 04 05 07 08 16
%e 12 : 02 03 04 06 07 08 16
%e 13 : 02 03 05 06 07 08 16
%e 14 : 02 04 05 06 07 08 16
%e 15 : 03 04 05 06 07 08 16
%e 16 : 09 10 11 12 13 14 15
%Y 7-regular simple graphs with girth at least 4: this sequence (connected), A185274 (disconnected), A185374 (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), A058275 (k=5), A058276 (k=6), this sequence (k=7), A181154 (k=8), A181170 (k=9).
%Y Connected 7-regular simple graphs with girth at least g: A014377 (g=3), this sequence (g=4).
%Y Connected 7-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4).
%K nonn,more,hard
%O 0,10
%A Jason Kimberley, last week of Jan 2011
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