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A368262
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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 two tiles that are each fixed under 180-degree rotation.
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2
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2, 3, 3, 6, 7, 4, 10, 24, 16, 6, 20, 76, 104, 43, 8, 36, 288, 720, 570, 120, 13, 72, 1072, 5600, 8356, 3408, 382, 18, 136, 4224, 43968, 131976, 105376, 22284, 1236, 30, 272, 16576, 350592, 2099728, 3359552, 1400536, 150824, 4243, 46
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OFFSET
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1,1
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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 | 2 3 6 10 20 36
2 | 3 7 24 76 288 1072
3 | 4 16 104 720 5600 43968
4 | 6 43 570 8356 131976 2099728
5 | 8 120 3408 105376 3359552 107390592
6 | 13 382 22284 1400536 89505968 5726776672
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MATHEMATICA
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A368262[n_, m_] := 1/(2n)*(DivisorSum[n, Function[d, EulerPhi[d]*2^(n*m/d)]] + n*2^(n*m/2)*Which[EvenQ[m], 1, EvenQ[n], 3/2, True, Sqrt[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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