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

1,107

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

Example

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;

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).

Sequence in context: A257228 A065803 A160540 * A319625 A307802 A169585

Adjacent sequences: A186715 A186716 A186717 * A186719 A186720 A186721

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Nov 28 2011

Status

approved