A391819 Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, all corners 1, and no 1 having more than two 1's adjacent.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 5, 2, 1, 1, 4, 9, 9, 4, 1, 1, 6, 17, 13, 17, 6, 1, 1, 10, 39, 29, 29, 39, 10, 1, 1, 16, 95, 87, 73, 87, 95, 16, 1, 1, 26, 217, 299, 265, 265, 299, 217, 26, 1, 1, 42, 473, 917, 1200, 1053, 1200, 917, 473, 42, 1, 1, 68, 1011, 2589, 4888, 5766, 5766, 4888, 2589, 1011, 68, 1

Offset

1,8

Links

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

Formula

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

Example

Array begins:
================================================
n\k | 1  2   3   4    5     6      7       8 ...
----+-------------------------------------------
  1 | 1  1   1   1    1     1      1       1 ...
  2 | 1  1   2   2    4     6     10      16 ...
  3 | 1  2   5   9   17    39     95     217 ...
  4 | 1  2   9  13   29    87    299     917 ...
  5 | 1  4  17  29   73   265   1200    4888 ...
  6 | 1  6  39  87  265  1053   5766   30600 ...
  7 | 1 10  95 299 1200  5766  39682  280496 ...
  8 | 1 16 217 917 4888 30600 280496 2648614 ...
   ...

Crossrefs

Main diagonal is A163732.

Rows 1..10 are A000012, A163733, A163734, A163735, A163736, A163737, A163738, A163739, A163740, A163741.

Cf. A389687, A391818, A391820, A391822.

Sequence in context: A245185 A034853 A242093 * A350910 A390207 A322058

Adjacent sequences: A391816 A391817 A391818 * A391820 A391821 A391822

Keyword

nonn,tabl

Author

Andrew Howroyd, Dec 21 2025

Status

approved