cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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).

Original entry on oeis.org

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

Views

Author

Andrew Howroyd, Feb 24 2023

Keywords

Comments

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

Examples

			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).

A360867 Number of unlabeled connected loopless multigraphs with n edges and degree >= 3 at each node.

Original entry on oeis.org

0, 0, 1, 1, 2, 6, 12, 32, 92, 273, 869, 2989, 10722, 40599
Offset: 1

Views

Author

Andrew Howroyd, Feb 24 2023

Keywords

Crossrefs

Row sums of A360866.
Cf. A076864, A360863 (loops allowed), A360868, A360869 (not necessarily connected).

Formula

Inverse Euler transform of A360869.
Showing 1-2 of 2 results.