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A127870
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Number of tilings of a 4xn 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, 33, 195, 2023, 16839, 151817, 1328849, 11758369, 103628653, 914646205, 8068452381, 71189251649, 628067760289, 5541284098945, 48888866203241, 431331449340441, 3805499681885145, 33574725778806817, 296219181642118401
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| 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
| S. Heubach, Tiling with Ls and Squares.
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FORMULA
| generating function = (1 - 4 z - 6 z^2 - 10 z^3 - 8 z^4 - 4 z^5)/(1 - 5z - 34 z^2 - 6 z^3 + 72 z^4 + 28 z^5 - 74 z^6 + 10 z^7 + 4 z^8 + 4 z^9)
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EXAMPLE
| a(2) = 33 because the 4x2 board can be tiled in one way with only square tiles, in 12 ways using one L-tile and 5 square tiles and in 20 ways with 2 L-tiles and 2 square tiles.
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MATHEMATICA
| Table[Coefficient[Normal[Series[(1 - 4 z - 6 z^2 - 10 z^3 - 8 z^4 - 4 z^5)/(1 - 5z - 34 z^2 - 6 z^3 + 72 z^4 + 28 z^5 - 74 z^6 + 10 z^7 + 4 z^8 + 4 z^9), {x, 0, 30}]], x, n], {n, 0, 30}]
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CROSSREFS
| Cf. A127864, A127865, A127866, A127867, A127868, A127869.
Sequence in context: A046142 A135827 A189180 * A142993 A075040 A178448
Adjacent sequences: A127867 A127868 A127869 * A127871 A127872 A127873
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KEYWORD
| nonn
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AUTHOR
| Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007
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