A360866 Triangle read by rows: T(n,k) is the number of unlabeled connected loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 2, 1 <= k <= floor(2*n/3).

0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 4, 7, 0, 1, 6, 19, 6, 0, 1, 8, 40, 37, 6, 0, 1, 10, 71, 135, 56, 0, 1, 12, 117, 366, 338, 35, 0, 1, 15, 184, 858, 1417, 494, 20, 0, 1, 17, 270, 1778, 4670, 3494, 492, 0, 1, 20, 387, 3413, 13125, 17355, 6047, 251

Offset

2,11

Comments

Terms may be computed using the tools geng, vcolg and multig in nauty with some additional processing to check the degrees of nodes.

Links

Table of n, a(n) for n=2..66.

Brendan McKay and Adolfo Piperno, nauty and Traces.

Example

Triangle begins:
  0;
  0, 1;
  0, 1;
  0, 1,  1;
  0, 1,  3,   2;
  0, 1,  4,   7;
  0, 1,  6,  19,    6;
  0, 1,  8,  40,   37,     6;
  0, 1, 10,  71,  135,    56;
  0, 1, 12, 117,  366,   338,    35;
  0, 1, 15, 184,  858,  1417,   494,   20;
  0, 1, 17, 270, 1778,  4670,  3494,  492;
  0, 1, 20, 387, 3413, 13125, 17355, 6047, 251;
  ...

Crossrefs

Row sums are A360867.

Diagonal sums are A360868.

Cf. A046752, A191646, A360862 (loops allowed).

Sequence in context: A348966 A008783 A139144 * A373451 A081576 A330785

Adjacent sequences: A360863 A360864 A360865 * A360867 A360868 A360869

Keyword

nonn,tabf

Author

Andrew Howroyd, Feb 24 2023

Status

approved