A366399 Triangle read by rows: T(n,k) is the number of paths traveling orthogonally on an n X k grid that visit every cell.

1, 1, 4, 1, 8, 20, 1, 14, 62, 276, 1, 22, 132, 1006, 4324, 1, 32, 336, 3610, 26996, 229348, 1, 44, 688, 12010, 109722, 1620034, 13535280, 1, 58, 1578, 38984, 602804, 12071462, 175905310, 3023313284, 1, 74, 3190, 122188, 2434670, 82550864, 1449655468, 43551685370, 745416341496

Offset

1,3

Links

Table of n, a(n) for n=1..45.

Example

T(n,k) is a triangular array read by rows:
  1,
  1,  4,
  1,  8, 20,
  1, 14, 62, 276,
  ...
T(2,2) = 4:
  +---+---+  +---+---+  +---+---+  +---+---+
  |   |   |  |   |   |  |   |   |  |   |   |
  | **|** |  | * | * |  | **|** |  | **|** |
  |   | * |  | * | * |  | * |   |  | * | * |
  +---+---+  +---+---+  +---+---+  +---+---+
  |   | * |  | * | * |  | * |   |  | * | * |
  | **|** |  | **|** |  | **|** |  | * | * |
  |   |   |  |   |   |  |   |   |  |   |   |
  +---+---+  +---+---+  +---+---+  +---+---+

Crossrefs

See A332307 for another version.

Cf. A120443 (T(n,n)), A366411 (row sums).

Sequence in context: A013611 A297194 A077910 * A100235 A089072 A348595

Adjacent sequences: A366396 A366397 A366398 * A366400 A366401 A366402

Keyword

tabl,nonn,walk

Author

Douglas Boffey, Oct 09 2023

Extensions

More terms (using A332307) from Pontus von Brömssen, Oct 09 2023

Status

approved