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A368218
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Table read by antidiagonals downward: T(n,k) is the number of tilings of the n X k grid up to horizontal and vertical reflections by a tile that is fixed under horizontal reflection only.
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7
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1, 3, 2, 4, 7, 3, 10, 20, 24, 6, 16, 76, 144, 76, 10, 36, 272, 1120, 1056, 288, 20, 64, 1072, 8448, 16576, 8320, 1072, 36, 136, 4160, 66816, 262656, 263680, 65792, 4224, 72, 256, 16576, 528384, 4197376, 8396800, 4197376, 525312, 16576, 136
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history;
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Table begins:
n\k | 1 2 3 4 5 6
----+--------------------------------------------
1 | 1 3 4 10 16 36
2 | 2 7 20 76 272 1072
3 | 3 24 144 1120 8448 66816
4 | 6 76 1056 16576 262656 4197376
5 | 10 288 8320 263680 8396800 268517376
6 | 20 1072 65792 4197376 268451840 17180065792
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MATHEMATICA
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A368218[n_, m_] := 2^(n*m/2 - 2)*(2^(n*m/2) + Boole[EvenQ[n*m]] + Boole[EvenQ[m]] + If[EvenQ[n], 1, 2^(m/2)])
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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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