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.

Showing 1-4 of 4 results.

A360863 Number of unlabeled connected multigraphs with n edges and degree >= 3 at each node, loops allowed.

Original entry on oeis.org

0, 1, 3, 5, 13, 36, 99, 301, 980, 3345, 12036, 45399, 178420, 729149
Offset: 1

Views

Author

Andrew Howroyd, Feb 24 2023

Keywords

Crossrefs

Row sums of A360862.
Cf. A360864 (by circuit rank), A360865 (not necessarily connected).

Formula

Inverse Euler transform of A360865.

A360862 Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3).

Original entry on oeis.org

1, 1, 2, 1, 4, 1, 7, 5, 1, 10, 20, 5, 1, 14, 48, 36, 1, 18, 99, 153, 30, 1, 23, 181, 481, 277, 17, 1, 28, 303, 1239, 1451, 323, 1, 34, 479, 2811, 5572, 2946, 193, 1, 40, 726, 5805, 17607, 17343, 3806, 71, 1, 47, 1055, 11148, 48401, 77708, 36872, 3188, 1, 54, 1492, 20219, 120018, 288476, 243007, 54386, 1496
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:
  1;
  1,  2;
  1,  4;
  1,  7,    5;
  1, 10,   20,     5;
  1, 14,   48,    36;
  1, 18,   99,   153,     30;
  1, 23,  181,   481,    277,     17;
  1, 28,  303,  1239,   1451,    323;
  1, 34,  479,  2811,   5572,   2946,    193;
  1, 40,  726,  5805,  17607,  17343,   3806,    71;
  1, 47, 1055, 11148,  48401,  77708,  36872,  3188;
  1, 54, 1492, 20219, 120018, 288476, 243007, 54386, 1496;
  ...
		

Crossrefs

Column 2 is A014616.
Row sums are A360863.
Diagonal sums are A360864.
Cf. A322115, A327615, A360866 (loopless).

A360879 Number of unlabeled nonseparable (or 2-connected) loopless multigraphs with circuit rank n and degree >= 3 at each node.

Original entry on oeis.org

0, 1, 4, 17, 118, 1198, 17133, 311757, 6803203
Offset: 1

Views

Author

Andrew Howroyd, Feb 25 2023

Keywords

Crossrefs

Diagonal sums of A046752.

Formula

a(n) = Sum_{k=2..2*n-2} A046752(n + k - 1, k).

Extensions

a(8) from the paper by Martin Dowd (2014) and a(9) from Martin Dowd (personal communication) added by Andrey Zabolotskiy, Feb 21 2024

A360868 Number of unlabeled connected loopless multigraphs with circuit rank n and degree >= 3 at each node.

Original entry on oeis.org

0, 1, 4, 23, 172, 1848, 25684
Offset: 1

Views

Author

Andrew Howroyd, Feb 25 2023

Keywords

Crossrefs

Diagonal sums of A360866.

Formula

a(n) = Sum_{k>=1} A360866(n + k - 1, k).
Showing 1-4 of 4 results.