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 1-5 of 5 results.

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).

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).

A360871 Number of unlabeled nonseparable (or 2-connected) multigraphs with n edges and degree >= 3 at each node, loops allowed.

Original entry on oeis.org

0, 0, 2, 4, 9, 20, 44, 113, 329, 1044, 3622, 13544, 53596, 223084, 969158
Offset: 1

Views

Author

Andrew Howroyd, Feb 25 2023

Keywords

Comments

A single-edge is considered to be nonseparable here.

Examples

			The a(3) = 2 multigraphs are:
  - a triple edge;
  - a single edge with a loop at each vertex.
		

Crossrefs

Row sums of A360870.

A360869 Number of unlabeled loopless multigraphs with n edges and degree >= 3 at each node.

Original entry on oeis.org

0, 0, 1, 1, 2, 7, 13, 35, 101, 295, 928, 3168, 11247, 42263
Offset: 1

Views

Author

Andrew Howroyd, Feb 25 2023

Keywords

Crossrefs

Cf. A050535, A360865 (loops allowed), A360867 (connected).

Formula

Euler transform of A360867.

A360882 Number of unlabeled connected multigraphs with n edges, no cut-points and degree >= 3 at each node, loops allowed.

Original entry on oeis.org

0, 1, 3, 5, 10, 21, 45, 114, 330, 1045, 3623, 13545, 53597, 223085, 969159
Offset: 1

Views

Author

Andrew Howroyd, Feb 27 2023

Keywords

Examples

			The a(3) = 3 multigraphs are:
  - a single vertex with 3 loops;
  - a triple edge;
  - a single edge with a loop at each vertex.
		

Crossrefs

Row sums of A360870.

Formula

a(n) = A360871(n) + 1 for n > 1.
Showing 1-5 of 5 results.