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 A186715 Irregular triangle C(n,k)=number of connected k-regular graphs on n vertices having girth at least five. 15

%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 k-regular 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.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&lt;137::AID-JGT7&gt;3.0.CO;2-G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137-146. [_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_k-reg_girth_ge_g_index">Index of sequences counting connected k-regular 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 k-regular 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 k-regular 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 k-regular 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

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Last modified March 18 17:51 EDT 2019. Contains 321292 sequences. (Running on oeis4.)