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

Author

Jason Kimberley, Jan 09 2012

Keywords

• nonn
• hard
• tabf

Comments

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

Examples

			                  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;
		

Links

• 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

Crossrefs

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).

Extensions

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