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%I #30 May 01 2014 02:39:59
%S 1,1,1,3,2,13,5,1,63,20,2,399,101,8,1,3268,743,48,1,33496,7350,450,5,
%T 412943,91763,5751,32,5883727,1344782,90553,385,94159721,22160335,
%U 1612905,7573,1,1661723296,401278984,31297357,181224,3,31954666517
%N Irregular triangle C(n,g) counting connected trivalent simple graphs on 2n vertices with girth exactly g.
%C The first column is for girth exactly 3. The row length is incremented to g-2 when 2n reaches A000066(g).
%H F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, <a href="http://alexandria.tue.nl/repository/books/252909.pdf">Computer investigations of cubic graphs</a>, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>
%e 1;
%e 1, 1;
%e 3, 2;
%e 13, 5, 1;
%e 63, 20, 2;
%e 399, 101, 8, 1;
%e 3268, 743, 48, 1;
%e 33496, 7350, 450, 5;
%e 412943, 91763, 5751, 32;
%e 5883727, 1344782, 90553, 385;
%e 94159721, 22160335, 1612905, 7573, 1;
%e 1661723296, 401278984, 31297357, 181224, 3;
%e 31954666517, 7885687604, 652159389, 4624480, 21;
%e 663988090257, 166870266608, 14499780660, 122089998, 545;
%e 14814445040728, 3781101495300, 342646718608, 3328899586, 30368;
%Y The sum of the n-th row of this sequence is A002851(n).
%Y Connected 3-regular simple graphs with girth exactly g: this sequence (triangle); chosen g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7).
%Y Connected 3-regular 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), A014376 (g=8).
%Y Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth exactly g: this sequence (k=3), A184940 (k=4), A184950 (k=5), A184960 (k=6), A184970 (k=7), A184980 (k=8).
%K nonn,hard,tabf
%O 2,4
%A _Jason Kimberley_, Nov 16 2011
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