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%I #29 Jan 28 2024 04:45:43
%S 1,2,1,5,2,19,6,1,85,22,2,509,110,9,1,4060,792,49,1,41301,7805,455,5,
%T 510489,97546,5783,32,7319447,1435720,90938,385,117940535,23780814,
%U 1620479,7574,1,2094480864,432757568,31478584,181227,3,40497138011,8542471494
%N Irregular triangle C(n,g) counting connected trivalent simple graphs on 2n vertices with girth at least g.
%C The first column is for girth at least 3. The row length is incremented to g-2 when 2n reaches A000066(g).
%H Jason Kimberley, <a href="/A185131/b185131.txt">Table of i, a(i) for i = 2..59 (n = 2..16)</a>
%H B. Brinkmann, J. Goedgebeur, and B. D. McKay, <a href="https://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_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 1;
%e 2, 1;
%e 5, 2;
%e 19, 6, 1;
%e 85, 22, 2;
%e 509, 110, 9, 1;
%e 4060, 792, 49, 1;
%e 41301, 7805, 455, 5;
%e 510489, 97546, 5783, 32;
%e 7319447, 1435720, 90938, 385;
%e 117940535, 23780814, 1620479, 7574, 1;
%e 2094480864, 432757568, 31478584, 181227, 3;
%e 40497138011, 8542471494, 656783890, 4624501, 21;
%e 845480228069, 181492137812, 14621871204, 122090544, 546, 1;
%e 18941522184590, 4127077143862, 345975648562, 3328929954, 30368, 0;
%e 453090162062723, ?, ?, 93990692595, 1782840, 1;
%e 11523392072541432, ?, ?, 2754222605376, 95079083, 3;
%e 310467244165539782, ?, ?, ?, 4686063120, 13;
%e 8832736318937756165, ?, ?, ?, 220323447962, 155;
%e ?, ?, ?, 10090653722861, 4337;
%Y Connected 3-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).
%Y Connected 3-regular 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).
%Y Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: this sequence (k=3), A184941 (k=4), A184951 (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8).
%K nonn,hard,tabf
%O 2,2
%A _Jason Kimberley_, Jan 09 2012
%E Terms C(18,6), C(20,7) and C(21,7) from House of Graphs via _Jason Kimberley_, May 21 2017
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