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A368263
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Table read by antidiagonals downward: T(n,k) is the number of tilings of the n X k cylinder up to 180-degree rotation by an asymmetric tile.
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3
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1, 3, 2, 4, 7, 2, 10, 20, 16, 4, 16, 76, 88, 43, 4, 36, 272, 720, 538, 120, 9, 64, 1072, 5472, 8356, 3280, 382, 10, 136, 4160, 43968, 131464, 105376, 22028, 1236, 22, 256, 16576, 349568, 2099728, 3355456, 1400536, 149800, 4243, 30
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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 | 2 16 88 720 5472 43968
4 | 4 43 538 8356 131464 2099728
5 | 4 120 3280 105376 3355456 107390592
6 | 9 382 22028 1400536 89489584 5726776672
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MATHEMATICA
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A368263[n_, m_] := 1/(2n)*(DivisorSum[n, EulerPhi[#]*2^(n*m/#) &] + n*2^(n*m/2)*Which[EvenQ[m], 1, EvenQ[n], 1/2, True, 0])
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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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