A184971 -id:A184971 - cp's OEIS frontend

A185131 Irregular triangle C(n,g) counting connected trivalent simple graphs on 2n vertices with girth at least g.

1, 2, 1, 5, 2, 19, 6, 1, 85, 22, 2, 509, 110, 9, 1, 4060, 792, 49, 1, 41301, 7805, 455, 5, 510489, 97546, 5783, 32, 7319447, 1435720, 90938, 385, 117940535, 23780814, 1620479, 7574, 1, 2094480864, 432757568, 31478584, 181227, 3, 40497138011, 8542471494

Offset: 2

Jason Kimberley, Jan 09 2012

The first column is for girth at least 3. The row length is incremented to g-2 when 2n reaches A000066(g).

			                  1;
                  2,             1;
                  5,             2;
                 19,             6,            1;
                 85,            22,            2;
                509,           110,            9,          1;
               4060,           792,           49,          1;
              41301,          7805,          455,          5;
             510489,         97546,         5783,         32;
            7319447,       1435720,        90938,        385;
          117940535,      23780814,      1620479,       7574,         1;
         2094480864,     432757568,     31478584,     181227,         3;
        40497138011,    8542471494,    656783890,    4624501,        21;
       845480228069,  181492137812,  14621871204,  122090544,       546,    1;
     18941522184590, 4127077143862, 345975648562, 3328929954,     30368,    0;
    453090162062723,        ?,            ?,     93990692595,   1782840,    1;
  11523392072541432,        ?,            ?,   2754222605376,  95079083,    3;
 310467244165539782,        ?,            ?,          ?,     4686063120,   13;
8832736318937756165,        ?,            ?,          ?,   220323447962,  155;
          ?,                ?,            ?,          ?, 10090653722861, 4337;

Jason Kimberley, Table of i, a(i) for i = 2..59 (n = 2..16)
B. Brinkmann, J. Goedgebeur, and B. D. McKay, Generation of cubic graphs, Discr. Math. Theor. Comp. Sci. 13 (2) (2011) 69-80.
House of Graphs, Cubic graphs
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
M. Meringer, Tables of Regular Graphs

Connected 3-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).
Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); chosen g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: this sequence (k=3), A184941 (k=4), A184951 (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8).

Terms C(18,6), C(20,7) and C(21,7) from House of Graphs via Jason Kimberley, May 21 2017

A184981 Irregular triangle C(n,g) counting the connected 8-regular simple graphs on n vertices with girth at least g.

Original entry on oeis.org

1, 1, 6, 94, 10786, 3459386, 1470293676, 733351105935, 1

Offset: 9

Jason Kimberley, Jan 19 2012

The first column is for girth at least 3. The row length is incremented to g-2 when n reaches A054760(8,g).

			1;
1;
6;
94;
10786;
3459386;
1470293676;
733351105935, 1;
?, 0;
?, 1;
?, 0;
?, 13;
?, 1;

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

Connected 8-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A014378 (g=3), A181154 (g=4).
Connected 8-regular simple graphs with girth exactly g: A184980 (triangle); chosen g: A184983 (g=3).
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), A184951 (k=5), A184961 (k=6), A184971 (k=7), this sequence (k=8), A184991 (k=9).

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).

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

Original entry on oeis.org

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

Offset: 3

Jason Kimberley, Jan 10 2012

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).

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

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

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).

a(14) from Jason Kimberley, Dec 26 2012

A184961 Irregular triangle C(n,g) read by rows, counting the connected 6-regular simple graphs on n vertices with girth at least g.

Original entry on oeis.org

1, 1, 4, 21, 266, 7849, 1, 367860, 0, 21609300, 1, 1470293675, 1, 113314233808, 9, 9799685588936, 6

Offset: 7

Jason Kimberley, Jan 10 2012

The first column is for girth at least 3. The row length sequence starts: 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3. The row length is incremented to g-2 when n reaches A054760(6,g).

			Triangle begins:
1;
1;
4;
21;
266;
7849, 1;
367860, 0;
21609300, 1;
1470293675, 1;
113314233808, 9;
9799685588936, 6;

Andries E. Brouwer, Cages
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Connected 6-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006822 (g=3), A058276 (g=4).
Connected 6-regular simple graphs with girth exactly g: A184960 (triangle); chosen g: A184963 (g=3), A184964 (g=4).
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), A184951 (k=5), this sequence (k=6), A184971 (k=7), A184981 (k=8).

A184970 Irregular triangle C(n,g) counting the connected 7-regular simple graphs on 2n vertices with girth exactly g.

Original entry on oeis.org

1, 5, 1547, 21609300, 1, 733351105933, 1

Offset: 4

Jason Kimberley, Feb 25 2011

The first column is for girth exactly 3. The row length sequence starts: 1, 1, 1, 2, 2, 2, 2, 2. The row length is incremented to g-2 when 2n reaches A054760(7,g).

			1;
5;
1547;
21609300, 1;
733351105933, 1;
?, 8;
?, 741;
?, 2887493;

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 = 4..11

Connected 7-regular simple graphs with girth at least g: A184971 (triangle); chosen g: A014377 (g=3), A181153 (g=4).
Connected 7-regular simple graphs with girth exactly g: this sequence (triangle); chosen g: A184973 (g=3), A184974 (g=4).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth exactly g: A198303 (k=3), A184940 (k=4), A184950 (k=5), A184960 (k=6), this sequence (k=7), A184980 (k=8).

A184991 Irregular triangle C(n,g) counting the connected 9-regular simple graphs on 2n vertices with girth at least g.

Original entry on oeis.org

1, 9, 88193, 113314233813

Offset: 5

Jason Kimberley, Feb 03 2012

The first column is for girth at least 3. The row length is incremented to g-2 when 2n reaches A054760(9,g).

			1;
 9;
 88193;
 113314233813;
 ?, 1;
 ?, 1;
 ?, 14;

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

Connected 9-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A014381 (g=3), A181170 (g=4).
Connected 9-regular simple graphs with girth exactly g: A184990 (triangle); chosen g: A184983 (g=3).
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), A184951 (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8), this sequence (k=9).

cp's OEIS Frontend

A185131 Irregular triangle C(n,g) counting connected trivalent simple graphs on 2n vertices with girth at least g.

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A184981 Irregular triangle C(n,g) counting the connected 8-regular simple graphs on n vertices with girth at least g.

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

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

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A184961 Irregular triangle C(n,g) read by rows, counting the connected 6-regular simple graphs on n vertices with girth at least g.

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A184970 Irregular triangle C(n,g) counting the connected 7-regular simple graphs on 2n vertices with girth exactly g.

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A184991 Irregular triangle C(n,g) counting the connected 9-regular simple graphs on 2n vertices with girth at least g.

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