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A368256
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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 horizontal and vertical reflections by a tile that is fixed under 180-degree rotation but not horizontal or vertical reflections.
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3
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1, 2, 2, 3, 5, 2, 6, 14, 9, 4, 10, 44, 52, 26, 4, 20, 152, 366, 298, 62, 8, 36, 560, 2800, 4244, 1704, 205, 9, 72, 2144, 22028, 66184, 52740, 11228, 623, 18, 136, 8384, 175296, 1050896, 1679776, 701124, 75412, 2171, 23
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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 2 3 6 10 20
2 | 2 5 14 44 152 560
3 | 2 9 52 366 2800 22028
4 | 4 26 298 4244 66184 1050896
5 | 4 62 1704 52740 1679776 53696936
6 | 8 205 11228 701124 44758448 2863442960
7 | 9 623 75412 9591666 1227199056 157073688884
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MATHEMATICA
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A368256[n_, m_] := 1/(4n)*( DivisorSum[n, EulerPhi[#]*2^(n*m/#) &] + n (2^(n*m/2 - 1))*Boole[EvenQ[n]] + If[EvenQ[m], DivisorSum[n, EulerPhi[#]*2^(n*m/LCM[#, 2]) &], DivisorSum[n, EulerPhi[#]*2^(n*m/#) &, EvenQ]] + 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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