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.

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.

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;
  ...

Links

Crossrefs

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

A360865 Number of unlabeled multigraphs with n edges and degree >= 3 at each node, loops allowed.

Original entry on oeis.org

0, 1, 3, 6, 16, 48, 130, 403, 1293, 4346, 15318, 56604, 217802, 873022
Offset: 1

Views

Author

Andrew Howroyd, Feb 24 2023

Keywords

Crossrefs

Cf. A360863 (connected).

Formula

Euler transform of A360863.

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.
Cf. A002935, A360863, 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

Cf. A002935, A360863, A360867, A360871.
Row sums of A360870.

Formula

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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