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A165799
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Number of tilings of a 4 X n rectangle using right trominoes and 2 X 2 tiles.
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6
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1, 0, 1, 4, 6, 16, 37, 92, 245, 560, 1426, 3720, 9069, 22808, 58177, 145660, 366318, 925536, 2331269, 5872212, 14802941, 37311528, 94038250, 236999064, 597348237, 1505640016, 3794761257, 9564393972, 24106951622, 60759989040, 153141435269, 385986293964
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OFFSET
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0,4
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..750
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FORMULA
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G.f.: -(6*x^3+x-1) / (4*x^9+16*x^7+22*x^6+3*x^5-x^4-9*x^3-x^2-x+1).
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EXAMPLE
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a(4) = 6, because there are 6 tilings of a 4 X 4 rectangle using right trominoes and 2 X 2 tiles:
.___.___. .___.___. .___.___. .___.___. .___.___. .___.___.
| . | . | | ._|_. | | ._| . | | ._|_. | | ._|_. | | . |_. |
|___|___| |_| . |_| |_| |___| |_| ._|_| |_|_. |_| |___| |_|
| . | . | | |___| | | |___| | | |_| . | | . |_| | | |___| |
|___|___| |___|___| |___|___| |___|___| |___|___| |___|___|
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MAPLE
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a:= n-> (Matrix([[4, 1, 0, 1, 0$5]]). Matrix(9, (i, j)-> if i=j-1 then 1 elif j=1 then [1, 1, 9, 1, -3, -22, -16, 0, -4][i] else 0 fi)^n)[1, 4]: seq (a(n), n=0..30);
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MATHEMATICA
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Series[ (-6*x^3 - x + 1) / (4*x^9 + 16*x^7 + 22*x^6 + 3*x^5 - x^4 - 9*x^3 - x^2 - x + 1), {x, 0, 31}] // CoefficientList[#, x] & (* Jean-François Alcover, Jun 18 2013, after Alois P. Heinz *)
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CROSSREFS
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Cf. A165791, A165716, A054854, A054856, A226322.
Column k=4 of A219946.
Sequence in context: A162485 A188466 A076066 * A056421 A032295 A072279
Adjacent sequences: A165796 A165797 A165798 * A165800 A165801 A165802
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KEYWORD
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easy,nice,nonn,changed
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AUTHOR
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Alois P. Heinz, Sep 27 2009
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STATUS
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approved
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