A184950 Irregular triangle C(n,g) counting the connected 5-regular simple graphs on 2n vertices with girth exactly g.

1, 3, 59, 1, 7847, 1, 3459376, 7, 2585136287, 388, 2807104844073, 406824

Offset: 3

Author

Jason Kimberley, Feb 24 2011

Keywords

• nonn
• hard
• more
• tabf

Comments

The first column is for girth exactly 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;
59, 1;
7847, 1;
3459376, 7;
2585136287, 388;
2807104844073, 406824;
?, 1125022325;
?, 3813549359274;
		

Links

• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g
• Jason Kimberley, Incomplete table of i, n, g, C(n,g)=a(i) for row n = 3..22

Crossrefs

Connected 5-regular simple graphs with girth at least g: A184951 (triangle); chosen g: A006821 (g=3), A058275 (g=4).

Connected 5-regular simple graphs with girth exactly g: this sequence (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 exactly g: A198303 (k=3), A184940 (k=4), this sequence (k=5), A184960 (k=6), A184970 (k=7), A184980 (k=8).