A373036 Triangle read by rows: T(n,k) is the number of edge subsets E of the n X k grid graph such that E contains a path between the top left node and the bottom right node, 1 <= k <= n.

1, 1, 7, 1, 40, 1135, 1, 216, 28942, 3329245, 1, 1144, 707239, 358911148, 167176484530, 1, 6016, 16963938, 37502829018, 74568672196498, 140386491543732211, 1, 31552, 403490839, 3856945416544, 32485805235240376, 256258754970108999490, 1946586793700869420041631

Offset: 1

Author

Pontus von Brömssen, May 20 2024

Keywords

• nonn
• tabl

Comments

T(n,k)/2^A151890(n-1,k-1) is the probability that the top left and bottom right vertices of the n X k grid graph are still connected after each edge has been independently deleted with probability 1/2.

Terms in the n-th row/column satisfies a linear recurrence with constant coefficients (probably of order A000245(n) or less).

Examples

			Triangle begins:
  1;
  1,    7;
  1,   40,     1135;
  1,  216,    28942,     3329245;
  1, 1144,   707239,   358911148,   167176484530;
  1, 6016, 16963938, 37502829018, 74568672196498, 140386491543732211;
  ...
		

Links

• Eugene Nonko, Table of n, a(n) for n = 1..105 (rows 1..14, terms 1..55 from Pontus von Brömssen)

Crossrefs

Cf. A000245, A151890, A349594 (2nd row/column), A349596 (3rd row/column) A365629 (4th row/column), A373037 (main diagonal).