A368264 Table read by downward antidiagonals: T(n,k) is the number of tilings of the n X k cylinder by two distinct tiles.
2, 4, 3, 8, 10, 4, 16, 36, 24, 6, 32, 136, 176, 70, 8, 64, 528, 1376, 1044, 208, 14, 128, 2080, 10944, 16456, 6560, 700, 20, 256, 8256, 87424, 262416, 209728, 43800, 2344, 36, 512, 32896, 699136, 4195360, 6710912, 2796976, 299600, 8230, 60
Offset: 1
Examples
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 24 176 1376 10944 87424 4 | 6 70 1044 16456 262416 4195360 5 | 8 208 6560 209728 6710912 214748416 6 | 14 700 43800 2796976 178962784 11453291200
Links
- Peter Kagey, Illustration of T(2,3)=36
- Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv: 2311.13072 [math.CO], 2023.
Programs
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Mathematica
A368264[n_, m_] := 1/n (DivisorSum[n, EulerPhi[#]*2^(n*m/#) &])