A184940 Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth exactly g.

1, 1, 2, 5, 1, 16, 0, 57, 2, 263, 2, 1532, 12, 10747, 31, 87948, 220, 803885, 1606, 8020590, 16828, 86027734, 193900, 983417704, 2452818, 11913817317, 32670329, 1, 152352034707, 456028472, 2, 2050055948375, 6636066091, 8, 28466137588780, 100135577616, 131

Offset

5,3

Comments

The first column is for girth exactly 3. The row length sequence starts: 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4. The row length is incremented to g-2 when n reaches A037233(g).

Links

Table of n, a(n) for n=5..41.

Jason Kimberley, Incomplete table of i, n, g, C(n,g)=a(i) for row n = 5..36

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

Example

1;
1;
2;
5, 1;
16, 0;
57, 2;
263, 2;
1532, 12;
10747, 31;
87948, 220;
803885, 1606;
8020590, 16828;
86027734, 193900;
983417704, 2452818;
11913817317, 32670329, 1;
152352034707, 456028472, 2;
2050055948375, 6636066091, 8;
28466137588780, 100135577616, 131;

Crossrefs

Connected 4-regular simple graphs with girth at least g: A184941 (triangle); chosen g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).

Connected 4-regular simple graphs with girth exactly g: this sequence (triangle); chosen g: A184943 (g=3), A184944 (g=4), A184945 (g=5), A184946 (g=6).

Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth exactly g: A198303 (k=3), this sequence (k=4), A184950 (k=5), A184960 (k=6), A184970 (k=7), A184980 (k=8).

Sequence in context: A119518 A216962 A186756 * A185140 A111797 A122104

Adjacent sequences: A184937 A184938 A184939 * A184941 A184942 A184943

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Feb 24 2011

Status

approved