cp's OEIS Frontend

A339070 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) graphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).

%I A339070 #20 Jan 04 2021 09:07:09
%S A339070 1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,1,2,1,0,0,0,0,3,3,1,0,0,0,0,2,9,4,
%T A339070 1,0,0,0,0,1,14,20,6,1,0,0,0,0,1,12,50,40,7,1,0,0,0,0,0,8,82,161,70,9,
%U A339070 1,0,0,0,0,0,5,94,429,433,121,11,1,0,0,0,0,0,2,81,780,1729,1034,189,13,1,0
%N A339070 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) graphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).
%H A339070 Hugo Pfoertner, <a href="/A339070/b339070.txt">Table of n, a(n) for n = 1..325</a> (rows 1..25, first 18 rows extracted from Robinson's tables, rows 19-20 from Andrew Howroyd)
%H A339070 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 IV, pages 4-9.
%F A339070 T(n, n) = 1 for n >= 3.
%F A339070 T(n, n-1) = A253186(n-3) for n >= 3.
%e A339070 Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
%e A339070   1;
%e A339070   0, 0;
%e A339070   0, 1, 0;
%e A339070   0, 0, 1, 0;
%e A339070   0, 0, 1, 1,  0;
%e A339070   0, 0, 1, 2,  1,  0;
%e A339070   0, 0, 0, 3,  3,  1,   0;
%e A339070   0, 0, 0, 2,  9,  4,   1,   0;
%e A339070   0, 0, 0, 1, 14, 20,   6,   1,   0;
%e A339070   0, 0, 0, 1, 12, 50,  40,   7,   1,  0;
%e A339070   0, 0, 0, 0,  8, 82, 161,  70,   9,  1, 0;
%e A339070   0, 0, 0, 0,  5, 94, 429, 433, 121, 11, 1, 0;
%e A339070   ...
%Y A339070 Row sums are A010355.
%Y A339070 Column sums are A002218.
%Y A339070 Cf. A054923, A123534, A253186, A339071 (transpose), A339160.
%K A339070 nonn,tabl
%O A339070 1,19
%A A339070 _Andrew Howroyd_, Nov 23 2020
%E A339070 First row and column removed by _Andrew Howroyd_, Dec 05 2020