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A278657
Number A(n,k) of tilings of a k X n rectangle using pentominoes of any shape and monominoes; square array A(n,k), n>=0, k>=0, read by antidiagonals.
11
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 1, 2, 25, 50, 25, 2, 1, 1, 3, 50, 311, 311, 50, 3, 1, 1, 4, 155, 1954, 4101, 1954, 155, 4, 1, 1, 5, 508, 11914, 56864, 56864, 11914, 508, 5, 1, 1, 6, 1343, 76003, 728857, 1532496, 728857, 76003, 1343, 6, 1
OFFSET
0,18
LINKS
Wikipedia, Pentomino
EXAMPLE
A(2,3) = A(3,2) = 7:
.___. .___. .___. .___. .___. .___. .___.
|_|_| | | | | | |_| |_| | | ._| |_. |
|_|_| | ._| |_. | | | | | | |_| |_| |
|_|_| |_|_| |_|_| |___| |___| |___| |___| .
.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 2, 3, ...
1, 1, 1, 7, 25, 50, 155, ...
1, 1, 7, 50, 311, 1954, 11914, ...
1, 1, 25, 311, 4101, 56864, 728857, ...
1, 2, 50, 1954, 56864, 1532496, 42238426, ...
1, 3, 155, 11914, 728857, 42238426, 2492016728, ...
CROSSREFS
Columns (or rows) k=0-7 give: A000012, A003520, A278874, A278875, A278876, A278456, A278877, A278878.
Sequence in context: A258149 A278717 A241009 * A242914 A046542 A172351
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Nov 25 2016
STATUS
approved