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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).

%I A360870 #14 Feb 27 2023 11:20:21
%S A360870 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 A360870 28,132,421,392,71,1,34,217,1008,1638,690,35,1,40,340,2210,5623,4548,
%U A360870 767,16,1,47,510,4477,16745,22657,8594,566,1,54,742,8557,44698,92844,64716,11247,226
%N 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).
%C A360870 Columns k >= 3 correspond to the 2-connected graphs.
%C A360870 Terms may be computed using the tools geng, vcolg and multig in nauty with some additional processing to check the degrees of nodes.
%H A360870 Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it/">nauty and Traces</a>.
%e A360870 Triangle begins:
%e A360870   1;
%e A360870   1,  2;
%e A360870   1,  4;
%e A360870   1,  7,   2;
%e A360870   1, 10,   8,    2;
%e A360870   1, 14,  19,   11;
%e A360870   1, 18,  40,   48,     7;
%e A360870   1, 23,  77,  154,    70,     5;
%e A360870   1, 28, 132,  421,   392,    71;
%e A360870   1, 34, 217, 1008,  1638,   690,    35;
%e A360870   1, 40, 340, 2210,  5623,  4548,   767,    16;
%e A360870   1, 47, 510, 4477, 16745, 22657,  8594,   566;
%e A360870   1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226;
%e A360870   ...
%Y A360870 Column 2 is A014616.
%Y A360870 Row sums are A360882.
%Y A360870 Row sums except first column are A360871.
%Y A360870 Cf. A046752, A322115, A360862, A360866.
%K A360870 nonn,tabf
%O A360870 2,3
%A A360870 _Andrew Howroyd_, Feb 25 2023