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

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..435

Formula

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

Example

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 ...
  ...

Crossrefs

Main diagonal is A163002.

Rows 1..10 are A000012, A048739(n-1), A163003, A163004, A163005, A163006, A163007, A163008, A163009, A163010.

Cf. A287151, A359574, A359575, A359576.

Sequence in context: A238688 A174117 A157210 * A359575 A034801 A331890

Adjacent sequences: A359570 A359571 A359572 * A359574 A359575 A359576

Keyword

nonn,tabl

Author

Andrew Howroyd, Jan 06 2023

Status

approved