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A226370
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Number of tilings of a 6 X n rectangle using integer-sided square tiles of area > 1.
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2
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1, 0, 1, 1, 3, 2, 7, 7, 16, 19, 40, 51, 98, 136, 245, 355, 617, 923, 1560, 2386, 3962, 6147, 10085, 15804, 25716, 40569, 65652, 104040, 167738, 266634, 428798, 683021, 1096560, 1749127, 2804915, 4478363, 7175960, 11464553, 18360713, 29346366, 46982101
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: 1/(1-x^2-x^3-2*x^4-x^6).
a(n) = a(n-2)+a(n-3)+2*a(n-4)+a(n-6) for n>5, a(0) = a(2) = a(3) = 1, a(1) = 0, a(4) = 3, a(5) = 2.
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EXAMPLE
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a(4) = 3:
._._._._. ._._._._. ._._._._.
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| | |___|___| |___|___|
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|_______| | | |___|___|
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|___|___| |_______| |___|___|
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MAPLE
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a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1,
`if`(i=6, [1, 0, 2, 1, 1, 0][j], 0)))^n. <<1, 0, 1, 1, 3, 2>>)[1, 1]:
seq(a(n), n=0..60);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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