A391489 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 top row to lower right corner.

1, 2, 1, 3, 5, 1, 4, 16, 12, 1, 5, 44, 82, 29, 1, 6, 113, 469, 416, 70, 1, 7, 281, 2502, 4776, 2103, 169, 1, 8, 688, 12966, 50720, 48047, 10633, 408, 1, 9, 1672, 66325, 522982, 1000725, 482895, 53767, 985, 1, 10, 4049, 337222, 5323854, 20172122, 19654292, 4854639, 271882, 2378, 1

Offset

1,2

Comments

The grid has m rows and n columns.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..435 (first 29 antidiagonals)

Example

Array begins:
=================================================================
 m\n| 1   2     3       4         5           6             7 ...
----+------------------------------------------------------------
  1 | 1   2     3       4         5           6             7 ...
  2 | 1   5    16      44       113         281           688 ...
  3 | 1  12    82     469      2502       12966         66325 ...
  4 | 1  29   416    4776     50720      522982       5323854 ...
  5 | 1  70  2103   48047   1000725    20172122     401252765 ...
  6 | 1 169 10633  482895  19654292   769984742   29719343543 ...
  7 | 1 408 53767 4854639 385935282 29335294083 2190944084653 ...
 ...

Crossrefs

Main diagonal is A163011.

Columns 1..10 are A000012, A000129(n+1), A163012, A163013, A163014, A163015, A163016, A163017, A163018, A163019.

Rows 1..10 are A000027, A048777(n-1), A163020, A163021, A163022, A163023, A163024, A163025, A163026, A163027.

Cf. A287151, A292357, A359573, A359574, A389687.

Sequence in context: A337886 A337884 A337883 * A202179 A297519 A297749

Adjacent sequences: A391486 A391487 A391488 * A391490 A391491 A391492

Keyword

nonn,tabl

Author

Andrew Howroyd, Dec 12 2025

Status

approved