A350913 -id:A350913 - cp's OEIS frontend

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

Andrew Howroyd, Jan 29 2022

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

			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;
  ...

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

Row sums are A350913.
Main diagonal is A000568.
The labeled version is A351263.
Cf. A051031 (graphs), A350910 (digraphs).

A351264 Number of oriented graphs on n labeled nodes whose underlying graph is regular.

Original entry on oeis.org

1, 1, 3, 9, 125, 1409, 134649, 9775233, 7056026001, 4365949239297, 25236968856946209, 97871747641444333569, 6214784730407041487304385, 252021162589018039813851873281, 105775796091843258520649528395263873, 37978893525907253948045960222247183810561

Offset: 0

Andrew Howroyd, Feb 05 2022

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..24

The unlabeled version is A350913.
Row sums of A351263.
Cf. A295193.

A350911 Number of regular digraphs on n unlabeled nodes.

Original entry on oeis.org

1, 1, 2, 3, 6, 11, 56, 609, 39346, 8728237, 6126648298, 14487876826313

Offset: 0

Andrew Howroyd, Jan 29 2022

Row sums of A350910.

Cf. A000273, A005176, A329234, A350913.

cp's OEIS Frontend

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.

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A351264 Number of oriented graphs on n labeled nodes whose underlying graph is regular.

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A350911 Number of regular digraphs on n unlabeled nodes.

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