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Search: id:A127865
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| A127865 |
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Number of square tiles in all tilings of a 2xn board with 1x1 and L-shaped tiles (where the L-shaped tiles cover 3 squares). |
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7
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| 2, 8, 30, 108, 354, 1152, 3614, 11204, 34170, 103176, 308598, 916236, 2702834, 7929872, 23155182, 67333140, 195082218, 563367960, 1622185958, 4658753564, 13347741666, 38160007200, 108881256414, 310108078116, 881761288154
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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P. Z. Chinn, R. Grimaldi and S. Heubach, Tiling with Ls and Squares, to appear in the Journal of Integer Sequences
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LINKS
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S. Heubach, Tiling with Ls and Squares.
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FORMULA
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a(n) = (2n - 12)(-1)^n + (2/3)[(9-5*Sqrt(3))(1+Sqrt(3))^n + (9+5*Sqrt(3))(1-Sqrt(3))^n] + (n/Sqrt(3))[(Sqrt(3)-1)(1+Sqrt(3))^n+ (Sqrt(3)+1)(1-Sqrt(3))^n]
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EXAMPLE
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a(2) = 8 because the 2 X 2 board can be tiled either with 4 squares or with a single L-shaped tile (in four orientations) together with a single square tile, and thus all the tilings of the 2 X 2 board contain 8 square tiles
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MATHEMATICA
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Table[(2n - 12)(-1)^n + (2/3)((9 - 5Sqrt[3])(1 + Sqrt[3])^n + (9 + 5Sqrt[3])(1 - Sqrt[3])^n) + (n/Sqrt[3])((Sqrt[3] - 1)( 1 + Sqrt[3])^n + (Sqrt[3] + 1)(1 - Sqrt[3])^n), {n, 1, 30}]
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CROSSREFS
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Cf. A127864, A127866, A127867, A127868, A127869, A127870, A127871, A127872.
Adjacent sequences: A127862 A127863 A127864 this_sequence A127866 A127867 A127868
Sequence in context: A052437 A131318 A010749 this_sequence A077839 A052530 A073663
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KEYWORD
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easy,nonn
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AUTHOR
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Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007
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