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A185131 Irregular triangle C(n,g) counting connected trivalent simple graphs on 2n vertices with girth at least g.

%I A185131 #35 Jan 09 2025 04:27:58
%S A185131 1,2,1,5,2,19,6,1,85,22,2,509,110,9,1,4060,792,49,1,41301,7805,455,5,
%T A185131 510489,97546,5783,32,7319447,1435720,90938,385,117940535,23780814,
%U A185131 1620479,7574,1,2094480864,432757568,31478584,181227,3,40497138011,8542471494
%N A185131 Irregular triangle C(n,g) counting connected trivalent simple graphs on 2n vertices with girth  at least g.
%C A185131 The first column is for girth at least 3. The row length is incremented to g-2 when 2n reaches A000066(g).
%H A185131 Jason Kimberley, <a href="/A185131/b185131.txt">Table of i, a(i) for i = 2..59 (n = 2..16)</a>
%H A185131 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 A185131 House of Graphs, <a href="https://houseofgraphs.org/meta-directory/cubic">Cubic graphs</a>
%H A185131 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 A185131 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%e A185131                   1;
%e A185131                   2,             1;
%e A185131                   5,             2;
%e A185131                  19,             6,            1;
%e A185131                  85,            22,            2;
%e A185131                 509,           110,            9,          1;
%e A185131                4060,           792,           49,          1;
%e A185131               41301,          7805,          455,          5;
%e A185131              510489,         97546,         5783,         32;
%e A185131             7319447,       1435720,        90938,        385;
%e A185131           117940535,      23780814,      1620479,       7574,         1;
%e A185131          2094480864,     432757568,     31478584,     181227,         3;
%e A185131         40497138011,    8542471494,    656783890,    4624501,        21;
%e A185131        845480228069,  181492137812,  14621871204,  122090544,       546,    1;
%e A185131      18941522184590, 4127077143862, 345975648562, 3328929954,     30368,    0;
%e A185131     453090162062723,        ?,            ?,     93990692595,   1782840,    1;
%e A185131   11523392072541432,        ?,            ?,   2754222605376,  95079083,    3;
%e A185131  310467244165539782,        ?,            ?,          ?,     4686063120,   13;
%e A185131 8832736318937756165,        ?,            ?,          ?,   220323447962,  155;
%e A185131           ?,                ?,            ?,          ?, 10090653722861, 4337;
%Y A185131 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 A185131 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 A185131 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 A185131 nonn,hard,tabf
%O A185131 2,2
%A A185131 _Jason Kimberley_, Jan 09 2012
%E A185131 Terms C(18,6), C(20,7) and C(21,7) from House of Graphs via _Jason Kimberley_, May 21 2017