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A014375 Number of trivalent connected simple graphs with 2n nodes and girth at least 7.

%I A014375 #33 Jul 08 2025 05:38:08
%S A014375 1,0,0,0,0,0,0,0,0,0,0,0,1,3,21,546,30368,1782840,95079083,4686063120,
%T A014375 220323447962,10090653722861
%N A014375 Number of trivalent connected simple graphs with 2n nodes and girth at least 7.
%C A014375 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]
%D A014375 CRC Handbook of Combinatorial Designs, 1996, p. 647.
%H A014375 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_7">Connected regular graphs with girth at least 7</a>
%H A014375 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 A014375 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%H A014375 M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199902)30:2&lt;137::AID-JGT7&gt;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_, May 29 2010]
%F A014375 a(n) = A006927(n) + A014376(n).
%Y A014375 From _Jason Kimberley_, May 29 2010 and Jan 29 2011: (Start)
%Y A014375 Connected k-regular simple graphs with girth at least 7: A186727 (any k), A186717 (triangle); specific k: A185117 (k=2), this sequence (k=3).
%Y A014375 Trivalent simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), this sequence (g=7), A014376 (g=8).
%Y A014375 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 A014375 nonn
%O A014375 0,14
%A A014375 _N. J. A. Sloane_
%E A014375 Terms a(17), a(18), and a(19) found by running Meringer's GENREG for 1.9 hours, 99.6 hours, and 207.8 processor days, at U. Ncle., by _Jason Kimberley_, May 29 2010
%E A014375 Terms a(20) and a(21) from House of Graphs via _Jason Kimberley_, May 21 2017