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A351322
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Number T(n,k) of tilings of a 3k X n rectangle with right trominoes.
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20
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1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 4, 0, 1, 1, 0, 8, 8, 4, 1, 1, 0, 16, 0, 18, 0, 1, 1, 0, 32, 64, 88, 72, 8, 1, 1, 0, 64, 0, 468, 384, 162, 0, 1, 1, 0, 128, 512, 2672, 8544, 4312, 520, 16, 1, 1, 0, 256, 0, 16072, 76800, 118586, 22656, 1514, 0, 1, 1, 0, 512, 4096, 100064, 1168512, 3403624, 1795360, 204184, 4312, 32, 1
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OFFSET
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0,9
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COMMENTS
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The table is read by descending antidiagonals.
If read by columns or rows:
Linear recurrences with different numbers of parameters are known for the sequences above.
Overview:
Constant Number of
side length Sequence parameters
2 T(2,k) 1
3 T(n,1),T(3,k) 2
8 T(8,k) >30
9 T(n,3),T(9,k) >30
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LINKS
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EXAMPLE
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6 X 2 rectangle: 4 tilings
___ ___ ___ ___
| _| | _| |_ | |_ |
|_| | |_| | | |_| | |_|
|___| |___| |___| |___|
| _| |_ | | _| |_ |
|_| | | |_| |_| | | |_|
|___| |___| |___| |___|
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Table T(n,k) begins:
n\k__0__1______2_________3_____________4
0: 1 1 1 1 1
1: 1 0 0 0 0
2: 1 2 4 8 16
3: 1 0 8 0 64
4: 1 4 18 88 468
5: 1 0 72 384 8544
6: 1 8 162 4312 118586
7: 1 0 520 22656 1795360
8: 1 16 1514 204184 29986082
9: 1 0 4312 1193600 467966840
10: 1 32 13242 9567192 7758809670
11: 1 0 39088 63112256 124693887784
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PROG
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(Maxima) See Maxima Code link.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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