A360882 -id:A360882

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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).

+10
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

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.

LINKS

Table of n, a(n) for n=2..66.

Brendan McKay and Adolfo Piperno, nauty and Traces.

EXAMPLE

Triangle begins:

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.

Cf. A046752, A322115, A360862, A360866.

KEYWORD

nonn,tabf

AUTHOR

Andrew Howroyd, Feb 25 2023

STATUS

approved

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