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%I #27 May 24 2017 08:32:44
%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,0,19,0,
%T 1272,25,494031,13504
%N Number of connected 4-regular simple graphs on n vertices with girth at least 6.
%C From _Jason Kimberley_, 2011: (Start)
%C The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth.
%C Does a(2n+1) ever exceed a(2n)?
%C (End)
%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>
%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%H M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137-146. [_Jason Kimberley_, Jan 29 2011]
%Y From _Jason Kimberley_, Jan 29 2011: (Start)
%Y Connected k-regular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: A185116 (k=2), A014374 (k=3), this sequence (k=4).
%Y Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), this sequence (g=6).
%Y Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
%K nonn,more,hard
%O 0,31
%A _N. J. A. Sloane_, Dec 17 2000
%E _Jason Kimberley_ inserted Meringer's computed terms a(n)=0 for n in [27,29,31,33] and appended terms a(35) and a(36), by running Meringer's GENREG for 17 and 106 processor days at U. Ncle, on May 04 2010.
%E a(37) appended from running GENREG for 450 processor days at U. Ncle. by _Jason Kimberley_, Dec 03 2011
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