A360870 Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes, no cut-points and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3).

1, 1, 2, 1, 4, 1, 7, 2, 1, 10, 8, 2, 1, 14, 19, 11, 1, 18, 40, 48, 7, 1, 23, 77, 154, 70, 5, 1, 28, 132, 421, 392, 71, 1, 34, 217, 1008, 1638, 690, 35, 1, 40, 340, 2210, 5623, 4548, 767, 16, 1, 47, 510, 4477, 16745, 22657, 8594, 566, 1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226

Offset

2,3

Comments

Columns k >= 3 correspond to the 2-connected graphs.

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:
  1;
  1,  2;
  1,  4;
  1,  7,   2;
  1, 10,   8,    2;
  1, 14,  19,   11;
  1, 18,  40,   48,     7;
  1, 23,  77,  154,    70,     5;
  1, 28, 132,  421,   392,    71;
  1, 34, 217, 1008,  1638,   690,    35;
  1, 40, 340, 2210,  5623,  4548,   767,    16;
  1, 47, 510, 4477, 16745, 22657,  8594,   566;
  1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226;
  ...

Crossrefs

Column 2 is A014616.

Row sums are A360882.

Row sums except first column are A360871.

Cf. A046752, A322115, A360862, A360866.

Sequence in context: A088522 A252751 A199744 * A115124 A115122 A097360

Adjacent sequences: A360867 A360868 A360869 * A360871 A360872 A360873

Keyword

nonn,tabf

Author

Andrew Howroyd, Feb 25 2023

Status

approved