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A360862 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).

%I A360862 #12 Feb 24 2023 16:28:03
%S A360862 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,
%T A360862 17,1,28,303,1239,1451,323,1,34,479,2811,5572,2946,193,1,40,726,5805,
%U A360862 17607,17343,3806,71,1,47,1055,11148,48401,77708,36872,3188,1,54,1492,20219,120018,288476,243007,54386,1496
%N A360862 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).
%C A360862 Terms may be computed using the tools geng, vcolg and multig in nauty with some additional processing to check the degrees of nodes.
%H A360862 Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it/">nauty and Traces</a>
%e A360862 Triangle begins:
%e A360862   1;
%e A360862   1,  2;
%e A360862   1,  4;
%e A360862   1,  7,    5;
%e A360862   1, 10,   20,     5;
%e A360862   1, 14,   48,    36;
%e A360862   1, 18,   99,   153,     30;
%e A360862   1, 23,  181,   481,    277,     17;
%e A360862   1, 28,  303,  1239,   1451,    323;
%e A360862   1, 34,  479,  2811,   5572,   2946,    193;
%e A360862   1, 40,  726,  5805,  17607,  17343,   3806,    71;
%e A360862   1, 47, 1055, 11148,  48401,  77708,  36872,  3188;
%e A360862   1, 54, 1492, 20219, 120018, 288476, 243007, 54386, 1496;
%e A360862   ...
%Y A360862 Column 2 is A014616.
%Y A360862 Row sums are A360863.
%Y A360862 Diagonal sums are A360864.
%Y A360862 Cf. A322115, A327615, A360866 (loopless).
%K A360862 nonn,tabf
%O A360862 2,3
%A A360862 _Andrew Howroyd_, Feb 24 2023