A391818 Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, a path of 1's from upper left corner to lower right corner, and no 1 having more than two 1's adjacent.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 8, 17, 8, 1, 1, 13, 39, 39, 13, 1, 1, 20, 83, 132, 83, 20, 1, 1, 32, 175, 389, 389, 175, 32, 1, 1, 52, 375, 1095, 1561, 1095, 375, 52, 1, 1, 85, 807, 3107, 5808, 5808, 3107, 807, 85, 1, 1, 138, 1732, 8790, 21608, 27874, 21608, 8790, 1732, 138, 1

Offset

1,5

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  3   5    8    13     20      32       52 ...
  3 | 1  5  17   39    83    175     375      807 ...
  4 | 1  8  39  132   389   1095    3107     8790 ...
  5 | 1 13  83  389  1561   5808   21608    81280 ...
  6 | 1 20 175 1095  5808  27874  132950   650001 ...
  7 | 1 32 375 3107 21608 132950  809249  5091285 ...
  8 | 1 52 807 8790 81280 650001 5091285 41309900 ...
  ...

Crossrefs

Main diagonal is A163684.

Rows 1..10 are A000012, A163685, A163686, A163687, A163688, A163689, A163690, A163691, A163692, A163693.

Cf. A359573, A391819, A391820, A391822.

Sequence in context: A347970 A296541 A056152 * A171229 A125690 A176481

Adjacent sequences: A391815 A391816 A391817 * A391819 A391820 A391821

Keyword

nonn,tabl

Author

Andrew Howroyd, Dec 20 2025

Status

approved