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A368987 Triangle read by rows: T(n,k) is the number of unlabeled point-determining graphs with n nodes and k edges, n >= 0, 0 <= k <= n*(n - 1)/2.

%I A368987 #11 Jan 18 2024 16:09:08
%S A368987 1,1,0,1,0,1,0,1,0,0,1,2,1,0,1,0,0,1,1,3,3,4,2,1,0,1,0,0,0,1,3,6,11,
%T A368987 14,13,12,9,5,2,1,0,1,0,0,0,1,1,5,15,31,50,77,89,94,83,61,37,24,11,5,
%U A368987 2,1,0,1,0,0,0,0,1,3,11,35,89,197,371,603,861,1068,1154,1098,926,679,445,257,134,65,30,11,5,2,1,0,1
%N A368987 Triangle read by rows: T(n,k) is the number of unlabeled point-determining graphs with n nodes and k edges, n >= 0, 0 <= k <= n*(n - 1)/2.
%C A368987 Point-determining graphs are also called mating graphs.
%H A368987 Andrew Howroyd, <a href="/A368987/b368987.txt">Table of n, a(n) for n = 0..175</a> (rows 0..10)
%H A368987 Ira M. Gessel and Ji Li, <a href="https://doi.org/10.1016/j.jcta.2010.03.009">Enumeration of point-determining graphs</a>, J. Combinatorial Theory Ser. A 118 (2011), 591-612.
%e A368987 Triangle begins:
%e A368987 [0] 1;
%e A368987 [1] 1;
%e A368987 [2] 0, 1;
%e A368987 [3] 0, 1, 0, 1;
%e A368987 [4] 0, 0, 1, 2, 1, 0,  1;
%e A368987 [5] 0, 0, 1, 1, 3, 3,  4,  2,  1,  0,  1;
%e A368987 [6] 0, 0, 0, 1, 3, 6, 11, 14, 13, 12,  9,  5,  2,  1,  0,  1;
%e A368987 [7] 0, 0, 0, 1, 1, 5, 15, 31, 50, 77, 89, 94, 83, 61, 37, 24, 11, 5, 2, 1, 0, 1;
%Y A368987 Row sums are A004110.
%Y A368987 Cf. A123551 (same row sums), A369283 (labeled).
%K A368987 nonn,tabf
%O A368987 0,12
%A A368987 _Andrew Howroyd_, Jan 15 2024