A270061 Number A(n,k) of tilings of a k X n rectangle using monominoes and trominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 2, 1, 1, 3, 14, 14, 3, 1, 1, 4, 45, 93, 45, 4, 1, 1, 6, 140, 590, 590, 140, 6, 1, 1, 9, 438, 3710, 7517, 3710, 438, 9, 1, 1, 13, 1371, 23509, 96176, 96176, 23509, 1371, 13, 1, 1, 19, 4287, 148796, 1238818, 2501946, 1238818, 148796, 4287, 19, 1

Offset

0,12

Links

Alois P. Heinz, Antidiagonals n = 0..25, flattened

Wikipedia, Tromino

Example

A(2,3) = A(3,2) = 14:
  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.
  |_____|  |_|_|_|  |_____|  |_| |_|  | |_|_|  | ._|_|  |_. |_|
  |_____|  |_____|  |_|_|_|  |___|_|  |___|_|  |_|_|_|  |_|_|_|
.
  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.
  |_|_|_|  | ._| |  | |_. |  |_|_| |  |_| |_|  |_| ._|  |_|_. |
  |_|_|_|  |_|___|  |___|_|  |_|___|  |_|___|  |_|_|_|  |_|_|_|  .
.
Square array A(n,k) begins:
  1, 1,   1,     1,       1,        1,          1, ...
  1, 1,   1,     2,       3,        4,          6, ...
  1, 1,   5,    14,      45,      140,        438, ...
  1, 2,  14,    93,     590,     3710,      23509, ...
  1, 3,  45,   590,    7517,    96176,    1238818, ...
  1, 4, 140,  3710,   96176,  2501946,   65410388, ...
  1, 6, 438, 23509, 1238818, 65410388, 3473827027, ...

Crossrefs

Columns (or rows) k=0-10 give: A000012, A000930, A270062, A270063, A270064, A270065, A270066, A270067, A270068, A270069, A270070.

Main diagonal gives A270071.

Cf. A233320.

Sequence in context: A196527 A064334 A320032 * A342059 A061176 A180957

Adjacent sequences: A270058 A270059 A270060 * A270062 A270063 A270064

Keyword

nonn,tabl

Author

Alois P. Heinz, Mar 09 2016

Status

approved