A359575 Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with a path of adjacent 1's from upper right corner to lower left corner.

1, 1, 1, 1, 3, 1, 1, 8, 8, 1, 1, 20, 51, 20, 1, 1, 49, 295, 295, 49, 1, 1, 119, 1632, 3828, 1632, 119, 1, 1, 288, 8830, 46557, 46557, 8830, 288, 1, 1, 696, 47239, 546286, 1225194, 546286, 47239, 696, 1, 1, 1681, 251261, 6279393, 30754544, 30754544, 6279393, 251261, 1681, 1

Offset: 1

Author

Andrew Howroyd, Jan 06 2023

Keywords

• nonn
• tabl

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    51     295      1632        8830         47239 ...
4  | 1  20   295    3828     46557      546286       6279393 ...
5  | 1  49  1632   46557   1225194    30754544     749866185 ...
6  | 1 119  8830  546286  30754544  1636193228   83949041929 ...
7  | 1 288 47239 6279393 749866185 83949041929 9009490924794 ...
  ...
		

Crossrefs

Main diagonal is A069343.

Rows 1..20 are A000012, A048739(n-1), A069325, A069326, A069327-A069342.

Cf. A359573, A359576.

Formula

T(m,n) = T(n,m).