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A230031
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Number A(n,k) of tilings of a k X n rectangle using tetrominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.
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18
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1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 4, 0, 4, 0, 1, 1, 0, 0, 23, 23, 0, 0, 1, 1, 0, 9, 0, 117, 0, 9, 0, 1, 1, 1, 0, 0, 454, 454, 0, 0, 1, 1, 1, 0, 25, 0, 2003, 0, 2003, 0, 25, 0, 1, 1, 0, 0, 997, 9157, 0, 0, 9157, 997, 0, 0, 1
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OFFSET
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0,24
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LINKS
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Alois P. Heinz, Antidiagonals n = 0..20, flattened
S. Butler, J. Ekstrand, S. Osborne, TETRIS Tiling, AMS Spring Central Sectional, Iowa State University, April 27-28 2013
R. S. Harris, Counting Polyomino Tilings
Wikipedia, Tetris
Wikipedia, Tetromino
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FORMULA
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A(n,k) = 0 <=> n*k mod 4 > 0.
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EXAMPLE
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A(4,2) = A(2,4) = 4:
._______. ._______. ._______. ._______.
| | | |_______| | |___. | | .___| |
|___|___| |_______| |_____|_| |_|_____|.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 0, 0, 0, 1, 0, 0, 0, 1, ...
1, 0, 1, 0, 4, 0, 9, 0, 25, ...
1, 0, 0, 0, 23, 0, 0, 0, 997, ...
1, 1, 4, 23, 117, 454, 2003, 9157, 40899, ...
1, 0, 0, 0, 454, 0, 0, 0, 800290, ...
1, 0, 9, 0, 2003, 0, 178939, 0, 22483347, ...
1, 0, 0, 0, 9157, 0, 0, 0, 657253434, ...
1, 1, 25, 997, 40899, 800290, 22483347, 657253434, 19077209438, ...
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CROSSREFS
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Columns (or rows) include: A000012, A007598, A232757, A174248, A232758, A232684, A232759, A232698, A247113, A232722.
Bisection of main diagonal (even part) gives A263425.
Cf. A099390, A233320, A233427.
Sequence in context: A147986 A147988 A306488 * A019920 A246130 A010675
Adjacent sequences: A230028 A230029 A230030 * A230032 A230033 A230034
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz, Nov 29 2013
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STATUS
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approved
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