A186718 - OEIS

%I #22 May 01 2014 02:39:58

%S 1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,

%T 0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,

%U 0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,3

%N Irregular triangle C(n,k): number of connected k-regular simple graphs on n vertices with girth at least eight.

%H Jason Kimberley, <a href="/A186718/b186718.txt">Table of i, a(i) for i = 1..151 (n = 1..47)</a>

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_8">Connected regular graphs with girth at least 8</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 1;

%e 0, 1;

%e 0, 0;

%e 0, 0;

%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;

%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;

%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, 0;

%e 0, 0, 1, 0;

%e 0, 0, 1, 1;

%e 0, 0, 1, 0;

%e 0, 0, 1, 3;

%e 0, 0, 1, 0;

%e 0, 0, 1, 13;

%e 0, 0, 1, 0;

%e 0, 0, 1, 155;

%e 0, 0, 1, 0;

%e 0, 0, 1, 4337;

%e 0, 0, 1, 0;

%e 0, 0, 1, 266362;

%e 0, 0, 1, 0;

%e 0, 0, 1, 20807688;

%e 0, 0, 1, 0;

%Y Connected k-regular simple graphs with girth at least 8: A186728 (any k), this sequence (triangle); specific k: A185118 (k=2), A014376 (k=3).

%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), A186716 (g=6), A186717 (g=7), this sequence (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 1,107

%A _Jason Kimberley_, Nov 28 2011