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A046752 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 3, 2 <= k <= floor(2*n/3).

%I A046752 #20 Feb 25 2023 18:07:57
%S A046752 1,1,1,1,1,2,2,1,3,5,1,4,13,4,1,6,26,24,5,1,7,47,84,38,1,9,78,233,216,
%T A046752 23,1,11,126,557,914,314,16,1,13,188,1193,3077,2270,325,1,15,276,2355,
%U A046752 8915,11592,4015,162,1,18,391,4370,23008,47079,31443,4495,66
%N A046752 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 3, 2 <= k <= floor(2*n/3).
%C A046752 Original name: Triangle of number of homeomorphically irreducible stars with n edges and m nodes.
%H A046752 Andrew Howroyd, <a href="/A046752/b046752.txt">Table of n, a(n) for n = 3..93</a> (rows 3..18)
%H A046752 B. R. Heap, <a href="https://doi.org/10.1063/1.1705068">The enumeration of homeomorphically irreducible star graphs</a>, J. Math. Phys., 7 (1966), 1582-1587.
%H A046752 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a046/A046752.java">Java program</a> (github).
%e A046752 Triangle begins:
%e A046752   1;
%e A046752   1;
%e A046752   1,  1;
%e A046752   1,  2,   2;
%e A046752   1,  3,   5;
%e A046752   1,  4,  13,    4;
%e A046752   1,  6,  26,   24,    5;
%e A046752   1,  7,  47,   84,   38;
%e A046752   1,  9,  78,  233,  216,    23;
%e A046752   1, 11, 126,  557,  914,   314,   16;
%e A046752   1, 13, 188, 1193, 3077,  2270,  325;
%e A046752   1, 15, 276, 2355, 8915, 11592, 4015, 162;
%e A046752   ...
%Y A046752 Row sums are A002935.
%Y A046752 Diagonal sums are A360879.
%Y A046752 Cf. A339160, A360866, A360870.
%K A046752 nonn,nice,tabf
%O A046752 3,6
%A A046752 _N. J. A. Sloane_
%E A046752 More terms from _Sean A. Irvine_, May 16 2020
%E A046752 Name edited and offset corrected by _Andrew Howroyd_, Feb 25 2023