A360870 - OEIS

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).

%I #14 Feb 27 2023 11:20:21

%S 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,

%T 28,132,421,392,71,1,34,217,1008,1638,690,35,1,40,340,2210,5623,4548,

%U 767,16,1,47,510,4477,16745,22657,8594,566,1,54,742,8557,44698,92844,64716,11247,226

%N 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).

%C Columns k >= 3 correspond to the 2-connected graphs.

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

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

%e Triangle begins:

%e 1;

%e 1, 2;

%e 1, 4;

%e 1, 7, 2;

%e 1, 10, 8, 2;

%e 1, 14, 19, 11;

%e 1, 18, 40, 48, 7;

%e 1, 23, 77, 154, 70, 5;

%e 1, 28, 132, 421, 392, 71;

%e 1, 34, 217, 1008, 1638, 690, 35;

%e 1, 40, 340, 2210, 5623, 4548, 767, 16;

%e 1, 47, 510, 4477, 16745, 22657, 8594, 566;

%e 1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226;

%e ...

%Y Column 2 is A014616.

%Y Row sums are A360882.

%Y Row sums except first column are A360871.

%Y Cf. A046752, A322115, A360862, A360866.

%K nonn,tabf

%O 2,3

%A _Andrew Howroyd_, Feb 25 2023