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Search: id:A127867
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| A127867 |
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Number of 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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| 1, 1, 11, 39, 195, 849, 3895, 17511, 79339, 358397, 1620843, 7326991, 33127155, 149766353, 677103839, 3061202815, 13839823275, 62570318397, 282882722979, 1278922980071, 5782057329219, 26140890761969, 118183916056327
(list; graph; listen)
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OFFSET
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0,3
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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 = (1-x)^2/(1-3x-7x^2+x^3-2x^4)
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EXAMPLE
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a(2) = 11 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.
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MATHEMATICA
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Table[Coefficient[Normal[Series[(1 - x)^2/(1 - 3x - 7x^2 + x^3 - 2x^4), {x, 0, 30}]], x, n], {n, 0, 30}]
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CROSSREFS
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Cf. A127864, A127865, A127866, A127868, A127869, A127870.
Sequence in context: A162261 A004188 A163634 this_sequence A138050 A077568 A122014
Adjacent sequences: A127864 A127865 A127866 this_sequence A127868 A127869 A127870
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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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