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%I #52 Feb 06 2024 05:11:42
%S 1,0,0,0,0,1,2,9,49,455,5783,90938,1620479,31478584,656783890,
%T 14621871204,345975648562
%N Number of trivalent connected simple graphs with 2n nodes and girth at least 5.
%C The null graph on 0 vertices is vacuously connected and 3-regular; since it is acyclic, it has infinite girth. - _Jason Kimberley_, Jan 29 2011
%C Brendan McKay has observed that a(13) = 31478584 is output by genreg, minibaum, and snarkhunter, but Meringer's table currently has a(13) = 31478582. - _Jason Kimberley_, May 17 2017
%D CRC Handbook of Combinatorial Designs, 1996, p. 647.
%H G. Brinkmann, J. Goedgebeur and B. D. McKay, <a href="https://dx.doi.org/10.46298/dmtcs.551">Generation of cubic graphs</a>, Discr. Math. Theor. Comp. Sci. 13 (2) (2011) 69-80.
%H House of Graphs, <a href="https://houseofgraphs.org/meta-directory/cubic">Cubic graphs</a>.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_5">Connected regular graphs with girth at least 5</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.
%Y Contribution from Jason Kimberley, 2010, 2011, and 2012: (Start)
%Y 3-regular simple graphs with girth at least 5: this sequence (connected), A185235 (disconnected), A185335 (not necessarily connected).
%Y Connected k-regular simple graphs with girth at least 5: A186725 (all k), A186715 (triangle); A185115 (k=2), this sequence (k=3), A058343 (k=4), A205295 (g=5).
%Y Connected 3-regular simple graphs with girth at least g: A185131 (triangle); A002851 (g=3), A014371 (g=4), this sequence (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).
%Y Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7). (End)
%K nonn,more,hard
%O 0,7
%A _N. J. A. Sloane_.
%E Terms a(15) and a(16) appended, from running Meringer's GENREG for 28.7 and 715.2 processor days at U. Ncle., by _Jason Kimberley_, Jun 28 2010.
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