A186718 Irregular triangle C(n,k): number of connected k-regular simple graphs on n vertices with girth at least eight.

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, 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, 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

Offset: 1

Author

Jason Kimberley, Nov 28 2011

Keywords

• nonn
• hard
• tabf

Examples

			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;
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, 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;
0, 0, 1, 0;
0, 0, 1, 13;
0, 0, 1, 0;
0, 0, 1, 155;
0, 0, 1, 0;
0, 0, 1, 4337;
0, 0, 1, 0;
0, 0, 1, 266362;
0, 0, 1, 0;
0, 0, 1, 20807688;
0, 0, 1, 0;
		

Links

• Jason Kimberley, Table of i, a(i) for i = 1..151 (n = 1..47)
• Jason Kimberley, Connected regular graphs with girth at least 8
• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Crossrefs

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

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).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth exactly g: A186733 (g=3), A186734 (g=4).