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

3,2

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).

Links

Table of n, a(n) for n=3..14.

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

Example

1;
3;
59, 1;
7847, 1;
3459376, 7;
2585136287, 388;
2807104844073, 406824;
?, 1125022325;
?, 3813549359274;

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).

Sequence in context: A024218 A049661 A295409 * A100611 A359069 A139882

Adjacent sequences: A184947 A184948 A184949 * A184951 A184952 A184953

Keyword

nonn,hard,more,tabf

Author

Jason Kimberley, Feb 24 2011

Status

approved