A389687 Array read by antidiagonals: T(n,m) is the number of n X m binary arrays with all 1's connected, and all corners 1.

1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 7, 12, 7, 1, 1, 17, 58, 58, 17, 1, 1, 41, 293, 540, 293, 41, 1, 1, 99, 1481, 5331, 5331, 1481, 99, 1, 1, 239, 7484, 53431, 101950, 53431, 7484, 239, 1, 1, 577, 37832, 536950, 1988608, 1988608, 536950, 37832, 577, 1, 1, 1393, 191285, 5398054, 39005563, 75185550, 39005563, 5398054, 191285, 1393, 1

Offset

1,8

Links

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

Formula

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

Example

Array begins:
===========================================================
n\k | 1  2    3      4        5          6            7 ...
----+------------------------------------------------------
  1 | 1  1    1      1        1          1            1 ...
  2 | 1  1    3      7       17         41           99 ...
  3 | 1  3   12     58      293       1481         7484 ...
  4 | 1  7   58    540     5331      53431       536950 ...
  5 | 1 17  293   5331   101950    1988608     39005563 ...
  6 | 1 41 1481  53431  1988608   75185550   2858390497 ...
  7 | 1 99 7484 536950 39005563 2858390497 210133770712 ...
   ...

Crossrefs

Main diagonal is A163046.

Columns 1..10 are A000012, A001333(n+1), A163047, A163048, A163049, A163050, A163051, A163052, A163053, A163054.

Cf. A287151, A292357, A359573, A359574.

Sequence in context: A375849 A364633 A333513 * A196646 A196601 A196578

Adjacent sequences: A389684 A389685 A389686 * A389688 A389689 A389690

Keyword

nonn,tabl

Author

Andrew Howroyd, Oct 26 2025

Status

approved