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

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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.

A360864 Number of unlabeled connected multigraphs with circuit rank n and degree >= 3 at each node, loops allowed.

Original entry on oeis.org

0, 3, 15, 111, 1076, 13870, 220520, 4185406, 92235118, 2314204852, 65129484278, 2032179006943, 69640160993587, 2600585852722150, 105127528809344785, 4574251821427917425, 213171992131468465801, 10593983324971249199532, 559293301762878627195807, 31259896932477899016109585, 1844062168535890557437809526
Offset: 1

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Author

Keywords

Comments

The terms up to a(21) were computed by Michael Borinsky and Jos Vermaseren using a program written in FORM. The graphs enumerated by a(n) are called admissible (Borinsky and Vogtmann, 2023).

Crossrefs

Diagonal sums of A360862.

Formula

a(n) = Sum_{k>=1} A360862(n + k - 1, k).

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).

A360870 Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes, no cut-points 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, 2, 1, 10, 8, 2, 1, 14, 19, 11, 1, 18, 40, 48, 7, 1, 23, 77, 154, 70, 5, 1, 28, 132, 421, 392, 71, 1, 34, 217, 1008, 1638, 690, 35, 1, 40, 340, 2210, 5623, 4548, 767, 16, 1, 47, 510, 4477, 16745, 22657, 8594, 566, 1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226
Offset: 2

Views

Author

Andrew Howroyd, Feb 25 2023

Keywords

Comments

Columns k >= 3 correspond to the 2-connected graphs.
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,   2;
  1, 10,   8,    2;
  1, 14,  19,   11;
  1, 18,  40,   48,     7;
  1, 23,  77,  154,    70,     5;
  1, 28, 132,  421,   392,    71;
  1, 34, 217, 1008,  1638,   690,    35;
  1, 40, 340, 2210,  5623,  4548,   767,    16;
  1, 47, 510, 4477, 16745, 22657,  8594,   566;
  1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226;
  ...
		

Crossrefs

Column 2 is A014616.
Row sums are A360882.
Row sums except first column are A360871.
Showing 1-4 of 4 results.