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A368259
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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 reflection by an asymmetric tile.
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3
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1, 2, 2, 4, 6, 2, 8, 20, 12, 4, 16, 72, 88, 39, 4, 32, 272, 688, 538, 104, 9, 64, 1056, 5472, 8292, 3280, 366, 10, 128, 4160, 43712, 131464, 104864, 22028, 1172, 22, 256, 16512, 349568, 2098704, 3355456, 1399512, 149800, 4179, 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 4 8 16 32
2 | 2 6 20 72 272 1056
3 | 2 12 88 688 5472 43712
4 | 4 39 538 8292 131464 2098704
5 | 4 104 3280 104864 3355456 107374208
6 | 9 366 22028 1399512 89489584 5726711136
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MATHEMATICA
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A368259[n_, m_]:=1/(2n) (DivisorSum[n, EulerPhi[#]*2^(n*m/#)&]+n*2^(n*m/2-1)*Boole[EvenQ[n]])
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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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