A184946 -id:A184946 - cp's OEIS frontend

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

Jason Kimberley, Feb 24 2011

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).

			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;

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

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).

A184941 Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth at least g.

Original entry on oeis.org

1, 1, 2, 6, 1, 16, 0, 59, 2, 265, 2, 1544, 12, 10778, 31, 88168, 220, 805491, 1606, 8037418, 16828, 86221634, 193900, 985870522, 2452818, 11946487647, 32670330, 1, 152808063181, 456028474, 2, 2056692014474, 6636066099, 8, 28566273166527, 100135577747, 131

Offset: 5

Jason Kimberley, Jan 10 2012

The first column is for girth at least 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).

			1;
1;
2;
6, 1;
16, 0;
59, 2;
265, 2;
1544, 12;
10778, 31;
88168, 220;
805491, 1606;
8037418, 16828;
86221634, 193900;
985870522, 2452818;
11946487647, 32670330, 1;
152808063181, 456028474, 2;
2056692014474, 6636066099, 8;
28566273166527, 100135577747, 131;

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

Connected 4-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).
Connected 4-regular simple graphs with girth exactly g: A184940 (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 at least g: A185131 (k=3), this sequence (k=4), A184951 (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8).

cp's OEIS Frontend

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

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