A359573 Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected and a path of 1's from upper left corner to lower right corner.
1, 1, 1, 1, 3, 1, 1, 8, 8, 1, 1, 20, 45, 20, 1, 1, 49, 234, 234, 49, 1, 1, 119, 1193, 2423, 1193, 119, 1, 1, 288, 6049, 24455, 24455, 6049, 288, 1, 1, 696, 30616, 245972, 482443, 245972, 30616, 696, 1, 1, 1681, 154861, 2473317, 9469361, 9469361, 2473317, 154861, 1681, 1
Offset: 1
Examples
Array begins: ================================================================ m\n| 1 2 3 4 5 6 7 ---+------------------------------------------------------------ 1 | 1 1 1 1 1 1 1 ... 2 | 1 3 8 20 49 119 288 ... 3 | 1 8 45 234 1193 6049 30616 ... 4 | 1 20 234 2423 24455 245972 2473317 ... 5 | 1 49 1193 24455 482443 9469361 185899132 ... 6 | 1 119 6049 245972 9469361 360923899 13742823032 ... 7 | 1 288 30616 2473317 185899132 13742823032 1012326365581 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..435
Crossrefs
Formula
T(m,n) = T(n,m).