%I
%S 1,0,1,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0,1,2,
%T 0,0,1,0,0,0,1,9,0,0,1,0,0,0,1,49,0,0,1,0,0,0,1,455,0,0,1,0,1,0,0,1,
%U 5783,2,0,0,1,0,8,0,0,1,90938,131,0,0,1,0,3917,0,0,1,1620479,123859
%N Irregular triangle C(n,k)=number of connected kregular graphs on n vertices having girth at least five.
%C Brendan McKay has observed that C(26,3) = 31478584 is output by genreg, minibaum, and snarkhunter, but Meringer's table currently has C(26,3) = 31478582.  _Jason Kimberley_, May 19 2017
%H Jason Kimberley, <a href="/A186715/b186715.txt">Table of i, a(i) for i = 1..111 (n = 1..28)</a>
%H M. Meringer, <a href="http://www.mathe2.unibayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%H M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)10970118(199902)30:2<137::AIDJGT7>3.0.CO;2G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137146. [_Jason Kimberley_, Jan 29 2011]
%H Jason Kimberley, <a href="/A186715/a186715.txt">Partial table of i, a(i) for i = 1..137 (n = 1..33)</a>
%H Jason Kimberley, <a href="/A186715/a186715_2.txt">Partial table of i, n, k, a(i)=C(n,k) for n = 1..33</a>
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_5">Connected regular graphs with girth at least 5</a>
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_kreg_girth_ge_g_index">Index of sequences counting connected kregular simple graphs with girth at least g</a>
%e 01: 1;
%e 02: 0, 1;
%e 03: 0, 0;
%e 04: 0, 0;
%e 05: 0, 0, 1;
%e 06: 0, 0, 1;
%e 07: 0, 0, 1;
%e 08: 0, 0, 1;
%e 09: 0, 0, 1;
%e 10: 0, 0, 1, 1;
%e 11: 0, 0, 1, 0;
%e 12: 0, 0, 1, 2;
%e 13: 0, 0, 1, 0;
%e 14: 0, 0, 1, 9;
%e 15: 0, 0, 1, 0;
%e 16: 0, 0, 1, 49;
%e 17: 0, 0, 1, 0;
%e 18: 0, 0, 1, 455;
%e 19: 0, 0, 1, 0, 1;
%e 20: 0, 0, 1, 5783, 2;
%e 21: 0, 0, 1, 0, 8;
%e 22: 0, 0, 1, 90938, 131;
%e 23: 0, 0, 1, 0, 3917;
%e 24: 0, 0, 1, 1620479, 123859;
%e 25: 0, 0, 1, 0, 4131991;
%e 26: 0, 0, 1, 31478584, 132160608;
%e 27: 0, 0, 1, 0, 4018022149;
%e 28: 0, 0, 1, 656783890, 118369811960;
%Y The row sums are given by A186725.
%Y Connected kregular simple graphs with girth at least 5: A186725 (all k), this sequence (triangle); A185115 (k=2), A014372 (k=3), A058343 (k=4), A205295 (k=5).
%Y Triangular arrays C(n,k) counting connected simple kregular graphs on n vertices with girth at least g: A068934 (g=3), A186714 (g=4), this sequence (g=5), A186716 (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).
%Y Triangular arrays C(n,k) counting connected simple kregular graphs on n vertices with girth exactly g: A186733 (g=3), A186734 (g=4).
%K nonn,hard,tabf
%O 1,34
%A _Jason Kimberley_, Oct 17 2011
