A350912 Triangle read by rows: T(n,k) is the number of oriented graphs on n unlabeled nodes whose underlying graph is k-regular, k = 0..n-1.

1, 1, 1, 1, 0, 2, 1, 1, 4, 4, 1, 0, 4, 0, 12, 1, 1, 12, 62, 112, 56, 1, 0, 18, 0, 1602, 0, 456, 1, 1, 40, 2062, 32263, 92980, 46791, 6880, 1, 0, 68, 0, 748576, 0, 11210264, 0, 191536, 1, 1, 140, 103827, 19349672, 616991524, 3319462470, 2729098064, 292115960, 9733056

Offset: 1

Author

Andrew Howroyd, Jan 29 2022

Keywords

• nonn
• tabl

Comments

The sum of the in-degree and out-degree at each node is k.

a(2*n,2*n-2) is the number of orientations (up to isomorphism) of the n-cocktail party graph. - Pontus von Brömssen, Apr 03 2022

Examples

			Triangle begins:
  1;
  1, 1;
  1, 0,  2;
  1, 1,  4,  4;
  1, 0,  4,  0,   12;
  1, 1, 12, 62,  112, 56;
  1, 0, 18,  0, 1602,  0, 456;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..253 (rows 1..22)

Crossrefs

Row sums are A350913.

Main diagonal is A000568.

The labeled version is A351263.

Cf. A051031 (graphs), A350910 (digraphs).