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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.
12
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
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
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Mar 09 2016
STATUS
approved