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A339072 Triangle read by rows: T(n,k) is the number of unlabeled simple 3-connected graphs with n nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n*(n-1)/2).

%I A339072 #8 Jan 31 2025 11:38:54
%S A339072 1,1,1,1,2,3,4,4,2,1,1,3,14,25,31,28,17,9,5,2,1,1,4,24,101,254,413,
%T A339072 475,426,306,187,103,52,23,11,5,2,1,1,19,204,1068,3348,7152,11199,
%U A339072 13683,13604,11374,8203,5216,2963,1536,737,333,144,62,25,11,5,2,1,1
%N A339072 Triangle read by rows: T(n,k) is the number of unlabeled simple 3-connected graphs with n nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n*(n-1)/2).
%H A339072 Andrew Howroyd, <a href="/A339072/b339072.txt">Table of n, a(n) for n = 4..732</a> (rows n=4..18, extracted from Robinson's tables)
%H A339072 R. W. Robinson, <a href="http://web.archive.org/web/20041220072855/http://www.cs.uga.edu/~rwr/publications/tables.pdf">Tables of 2-Connected and 3-Connected Graphs by Nodes and Edges</a>, Table VI, pages 19-27.
%e A339072 Triangle begins:
%e A339072 ===========================================================
%e A339072 n/k | 6  7  8   9  10 11  12  13  14  15  16 17 18 19 20 21
%e A339072 ----+------------------------------------------------------
%e A339072   4 | 1;
%e A339072   5 |       1,  1,  1;
%e A339072   6 |           2,  3, 4,  4,  2,  1,  1;
%e A339072   7 |                  3, 14, 25, 31, 28, 17, 9, 5, 2, 1, 1;
%e A339072   8 |                      4, 24 ...
%e A339072   ...
%Y A339072 Row sums are A006290.
%Y A339072 Column sums are A338511.
%Y A339072 Cf. A054924, A123542, A339071.
%K A339072 nonn,tabf
%O A339072 4,5
%A A339072 _Andrew Howroyd_, Nov 24 2020