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

2,2

Comments

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

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

Example

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;

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).

Sequence in context: A115345 A194092 A140165 * A199660 A367671 A141483

Adjacent sequences: A185128 A185129 A185130 * A185132 A185133 A185134

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Jan 09 2012

Extensions

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

Status

approved