login
A185131
Irregular triangle C(n,g) counting connected trivalent simple graphs on 2n vertices with girth at least g.
18
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
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
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
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