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).

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, 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, 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

Offset: 1

Author

Andrew Howroyd, Nov 23 2020

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
  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,   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,  1, 0;
  0, 0, 0, 0,  5, 94, 429, 433, 121, 11, 1, 0;
  ...
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..325 (rows 1..25, first 18 rows extracted from Robinson's tables, rows 19-20 from Andrew Howroyd)
• R. W. Robinson, Tables of 2-Connected and 3-Connected Graphs by Nodes and Edges, Table IV, pages 4-9.

Crossrefs

Row sums are A010355.

Column sums are A002218.

Cf. A054923, A123534, A253186, A339071 (transpose), A339160.

Formula

T(n, n) = 1 for n >= 3.

T(n, n-1) = A253186(n-3) for n >= 3.

Extensions

First row and column removed by Andrew Howroyd, Dec 05 2020