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A368258
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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 reflections by two tiles that are each fixed under horizontal reflection.
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2
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2, 4, 3, 8, 10, 4, 16, 36, 20, 6, 32, 136, 120, 55, 8, 64, 528, 816, 666, 136, 13, 128, 2080, 5984, 9316, 3536, 430, 18, 256, 8256, 45760, 139656, 106912, 23052, 1300, 30, 512, 32896, 357760, 2164240, 3371840, 1415896, 151848, 4435, 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 4 8 16 32 64
2 | 3 10 36 136 528 2080
3 | 4 20 120 816 5984 45760
4 | 6 55 666 9316 139656 2164240
5 | 8 136 3536 106912 3371840 107505280
6 | 13 430 23052 1415896 89751728 5730905440
7 | 18 1300 151848 19206736 2454791328 314154568000
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MATHEMATICA
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A368258[n_, m_] := 1/(2n)*(DivisorSum[n, EulerPhi[#]*2^(n*m/#)&] + n*2^(n*m/2)*If[EvenQ[n], 1/2*(2^m + 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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