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%I #38 Jun 03 2023 09:30:17
%S 1,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,
%T 0,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,5,0,0,1,0,0,0,1,32,0,0,1,0,0,0,1,
%U 385,0,0,1,0,0,0,1,7574,0,0,1,0,0,0,1,181227,1,0,0,1,0,0,0,0,1
%N Irregular triangle C(n,k): the number of connected k-regular graphs on n vertices having girth at least six.
%C Other than the first two rows, each row begins with 0, 0, 1.
%D M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.
%H Jason Kimberley, <a href="/A186716/b186716.txt">Rows n = 1..37 of triangle, flattened</a>
%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_6">Connected regular graphs with girth at least 6</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.
%e 1;
%e 0, 1;
%e 0, 0;
%e 0, 0;
%e 0, 0;
%e 0, 0, 1;
%e 0, 0, 1;
%e 0, 0, 1;
%e 0, 0, 1;
%e 0, 0, 1;
%e 0, 0, 1;
%e 0, 0, 1;
%e 0, 0, 1;
%e 0, 0, 1, 1;
%e 0, 0, 1, 0;
%e 0, 0, 1, 1;
%e 0, 0, 1, 0;
%e 0, 0, 1, 5;
%e 0, 0, 1, 0;
%e 0, 0, 1, 32;
%e 0, 0, 1, 0;
%e 0, 0, 1, 385;
%e 0, 0, 1, 0;
%e 0, 0, 1, 7574;
%e 0, 0, 1, 0;
%e 0, 0, 1, 181227, 1;
%e 0, 0, 1, 0, 0;
%e 0, 0, 1, 4624501, 1;
%e 0, 0, 1, 0, 0;
%e 0, 0, 1, 122090544, 4;
%e 0, 0, 1, 0, 0;
%e 0, 0, 1, 3328929954, 19;
%e 0, 0, 1, 0, 0;
%e 0, 0, 1, 93990692595, 1272;
%e 0, 0, 1, 0, 25;
%e 0, 0, 1, 2754222605376, 494031;
%e 0, 0, 1, 0, 13504;
%Y Connected k-regular simple graphs with girth at least 6: A186726 (any k), this sequence (triangle); specific k: A185116 (k=2), A014374 (k=3), A058348 (k=4).
%Y Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth at least g: A068934 (g=3), A186714 (g=4), A186715 (g=5), this sequence (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).
%Y Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth exactly g: A186733 (g=3), A186734 (g=4).
%K nonn,hard,tabf
%O 1,53
%A _Jason Kimberley_, Nov 23 2011
%E C(36,3) from House of Graphs via _Jason Kimberley_, May 21 2017
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