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A368255
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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 vertical reflections but not horizontal reflections.
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1
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1, 2, 2, 3, 5, 2, 6, 14, 9, 4, 10, 44, 50, 26, 4, 20, 152, 366, 298, 62, 9, 36, 560, 2780, 4244, 1692, 205, 10, 72, 2144, 22028, 66184, 52740, 11272, 623, 22, 136, 8384, 175128, 1050896, 1679368, 701124, 75486, 2171, 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 2 3 6 10 20
2 | 2 5 14 44 152 560
3 | 2 9 50 366 2780 22028
4 | 4 26 298 4244 66184 1050896
5 | 4 62 1692 52740 1679368 53696936
6 | 9 205 11272 701124 44761184 2863442960
7 | 10 623 75486 9591666 1227208420 157073688884
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MATHEMATICA
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A368255[n_, m_] := 1/(4n)*(DivisorSum[n, Function[d, EulerPhi[d]*2^(n*m/d)]] + n*(2^(n*m/2 - 1))*Boole[EvenQ[n]] + If[EvenQ[m], DivisorSum[n, Function[d, EulerPhi[d]*2^(n*m/LCM[d, 2])]], DivisorSum[n, Function[d, EulerPhi[d]*2^((n*m - n)/LCM[d, 2])*2^(n/d)]]] + 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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