%I #24 May 01 2014 02:38:03

%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,13,155,4337,266362,20807688

%N Number of trivalent connected simple graphs with 2n nodes and girth at least 8.

%D CRC Handbook of Combinatorial Designs, 1996, p. 647.

%D M. Meringer, Fast Generation of Regular Graphs and Construction of Cages</a>, Journal of Graph Theory, 30 (1999), 137-146 doi 10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G [From _Jason Kimberley_, Jan 29 2011]

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_8">Connected regular graphs with girth at least 8</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>

%Y Contribution from _Jason Kimberley_, May 18 2010 and Jan 29 2011: (Start)

%Y Connected k-regular simple graphs with girth at least 8: A186728 (any k), A186718 (triangle); specific k: A185118 (k=2), this sequence (k=3).

%Y Trivalent simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), this sequence (g=8).

%Y Trivalent simple graphs with girth exactly g: A198303 (triangle); chosen g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7). (End)

%K nonn,more,hard

%O 0,19

%A _N. J. A. Sloane_.

%E Terms a(21), a(22), and a(23) found by running Meringer's GENREG for 0.15, 5.0, and 176.2 processor days, respectively, at U. Ncle. by _Jason Kimberley_, May 18 2010