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Search: id:A127868
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| A127868 |
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Number of square 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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| 3, 30, 171, 1044, 5691, 30678, 159891, 821100, 4151511, 20764590, 102880755, 505866804, 2471159019, 12004723878, 58037429739, 279405305676, 1340130574407, 6406579480446, 30536794325547, 145166910196116
(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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generating function = 3x(1-x)^2(1+6x+3x^2)/(1-3x-7x^2+x^3-2x^4)^2
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EXAMPLE
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a(2) = 30 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 6 + 8 * 3=30 square tiles in all of the 3x2 tilings.
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MATHEMATICA
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Table[Coefficient[Normal[Series[3x(1-x)^2(1+6x+3x^2)/(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, A127869, A127870.
Sequence in context: A031205 A020874 A003689 this_sequence A002463 A013281 A013274
Adjacent sequences: A127865 A127866 A127867 this_sequence A127869 A127870 A127871
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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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