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A339069 Triangle read by rows: T(n,k) is the number of unlabeled simple series-reduced 2-connected graphs with n nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n*(n-1)/2).

%I A339069 #9 Jan 31 2025 11:39:09
%S A339069 1,1,1,1,2,4,5,4,2,1,1,4,17,30,34,29,17,9,5,2,1,1,5,33,133,307,464,
%T A339069 505,438,310,188,103,52,23,11,5,2,1,1,25,277,1352,3953,7939,11897,
%U A339069 14131,13827,11465,8235,5226,2966,1537,737,333,144,62,25,11,5,2,1,1
%N A339069 Triangle read by rows: T(n,k) is the number of unlabeled simple series-reduced 2-connected graphs with n nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n*(n-1)/2).
%H A339069 Andrew Howroyd, <a href="/A339069/b339069.txt">Table of n, a(n) for n = 4..732</a> (rows n=4..18, extracted from Robinson's tables)
%H A339069 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 V, pages 10-18.
%H A339069 R. W. Robinson and T. R. S. Walsh, <a href="https://doi.org/10.1006/jctb.1993.1022">Inversion of cycle index sum relations for 2- and 3-connected graphs</a>, J. Combin. Theory Ser. B. 57 (1993), 289-308.
%e A339069 Triangle begins:
%e A339069 ===========================================================
%e A339069 n/k | 6  7  8   9  10 11  12  13  14  15  16 17 18 19 20 21
%e A339069 ----+------------------------------------------------------
%e A339069   4 | 1;
%e A339069   5 |       1,  1,  1;
%e A339069   6 |           2,  4, 5,  4,  2,  1,  1;
%e A339069   7 |                  4, 17, 30, 34, 29, 17, 9, 5, 2, 1, 1;
%e A339069   8 |                      5, 33 ...
%e A339069   ...
%Y A339069 Row sums are A006289.
%Y A339069 Column sums are A339068.
%Y A339069 Cf. A123545, A123546, A339071, A339072.
%K A339069 nonn,tabf
%O A339069 4,5
%A A339069 _Andrew Howroyd_, Nov 24 2020