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A127864
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Number of tilings of a 2xn board with 1x1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).
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8
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1, 1, 5, 11, 33, 87, 241, 655, 1793, 4895, 13377, 36543, 99841, 272767, 745217, 2035967, 5562369, 15196671, 41518081, 113429503, 309895169, 846649343, 2313089025, 6319476735, 17265131521, 47169216511
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The signed version of this sequence appears as A077917
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LINKS
| P. Z. Chinn, R. Grimaldi and S. Heubach, Tiling with Ls and Squares, J. Int. Sequences 10 (2007) #07.2.8
S. Heubach, Tiling with Ls and Squares.
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FORMULA
| a(n) = a(n-1)+ 4 a(n-2) + 2 a(n-3); a(n) = (-1)^n +(1/Sqrt(3))*((1+Sqrt(3))^n - (1-Sqrt(3))^n); generating function 1/(1-x-4x^2-2x^3)
a(n) = A028860(n+2)+(-1)^n. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 29 2010]
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EXAMPLE
| a(2) = 5 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.
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MATHEMATICA
| Table[Coefficient[Normal[Series[ -1/( 2x^3 + 4x^2 + x - 1), {x, 0, 30}]], x, n], {n, 0, 30}]
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CROSSREFS
| Cf. A077917, A127865, A127866, A127867, A127868, A127869, A127870, A127871, A127872.
Sequence in context: A074648 A106908 A107442 * A077917 A055936 A194589
Adjacent sequences: A127861 A127862 A127863 * A127865 A127866 A127867
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KEYWORD
| easy,nonn
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AUTHOR
| Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007
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EXTENSIONS
| JIS reference updated by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2010
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