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Search: id:A127869
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| A127869 |
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Number of L-shaped tiles in all tilings of a 3xn board with 1x1 and L-shaped tiles (where the L-shaped tiles cover 3 squares). |
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7
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| 12, 60, 432, 2348, 13144, 69280, 361012, 1841736, 9286900, 46303316, 228903592, 1123242916, 5477879120, 26572232312, 128302070508, 616985221280, 2956362520140, 14120605179500, 67252176519008
(list; graph; listen)
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OFFSET
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2,1
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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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generating function = 4x^2(3-3x+3x^2-4x^3+x^4)/(1-3x-7x^2+x^3-2x^4)^2
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EXAMPLE
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a(2) = 12 because the 3x2 board can be tiled in one way with only square tiles, in 8 ways using one L-tile and 3 square tiles, and in 2 ways with 2 L-tiles, so there are altogether 8 + 2*2 =12 L- tiles in all of the 3x2 tilings.
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MATHEMATICA
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Table[Coefficient[Normal[Series[4x^2(3-3x+3x^2-4x^3+x^4)/(1-3x-7x^2+x^3-2x^4)^2, {x, 0, 30}]], x, n], {n, 0, 30}]
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CROSSREFS
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Cf. A127864, A127865, A127866, A127867, A127868, A127870.
Sequence in context: A009031 A009136 A053533 this_sequence A012518 A012315 A009062
Adjacent sequences: A127866 A127867 A127868 this_sequence A127870 A127871 A127872
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KEYWORD
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nonn
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AUTHOR
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Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007
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