A184951 Irregular triangle C(n,g) counting the connected 5-regular simple graphs on 2n vertices with girth at least g.

1, 3, 60, 1, 7848, 1, 3459383, 7, 2585136675, 388, 2807105250897, 406824

Offset: 3

Author

Jason Kimberley, Jan 10 2012

Keywords

• nonn
• hard
• more
• tabf

Comments

The first column is for girth at least 3. The row length sequence starts: 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4. The row length is incremented to g-2 when 2n reaches A054760(5,g).

Examples

			1;
3;
60, 1;
7848, 1;
3459383, 7;
2585136675, 388;
2807105250897, 406824;
		

Links

• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Crossrefs

Connected 5-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006821 (g=3), A058275 (g=4), A205295 (g=5).

Connected 5-regular simple graphs with girth exactly g: A184950 (triangle); chosen g: A184953 (g=3), A184954 (g=4), A184955 (g=5).

Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), A184941 (k=4), this sequence (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8).

Extensions

a(14) from Jason Kimberley, Dec 26 2012