proposed

approved

editing

proposed

Cf. A322115, A327615, A360866 (loopless).

proposed

editing

editing

proposed

Cf. A322115, A327615.

...

Column 2 is A014616.

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).

Terms may be computed using the tools geng, vcolg and multig in nauty with some additional process processing to check the degrees of nodes.

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

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

2,3

Terms may be computed using the tools geng, vcolg and multig in nauty with some additional process to check the degrees of nodes.

Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it/">nauty and Traces</a>

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;

Row sums are A360863.

Diagonal sums are A360864.

allocated

nonn,tabf

Andrew Howroyd, Feb 24 2023

approved

editing