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A226369
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Number of tilings of a 5 X n rectangle using integer-sided square tiles of area > 1.
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2
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1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 4, 4, 0, 0, 1, 6, 12, 8, 0, 1, 8, 24, 32, 16, 1, 10, 40, 80, 80, 33, 12, 60, 160, 240, 193, 78, 84, 280, 560, 673, 464, 240, 448, 1120, 1793, 1810, 1168, 928, 2016, 4033, 5396, 4788, 3264, 3872, 8065, 13462, 15580, 12840, 10400
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OFFSET
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0,7
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,2).
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FORMULA
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G.f.: 1/(1-x^5-2*x^6).
a(n) = a(n-5)+2*a(n-6) for n>5, a(0) = a(5) = 1, a(1) = a(2) = a(3) = a(4) = 0.
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EXAMPLE
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a(6) = 2:
._._._._._._. ._._._._._._.
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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, [2, 1, 0$4][j], 0)))^n. <<1, [0$4][], 1>>)[1, 1]:
seq(a(n), n=0..70);
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CROSSREFS
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Column k=5 of A226206.
Sequence in context: A191906 A187080 A301342 * A320751 A263764 A325668
Adjacent sequences: A226366 A226367 A226368 * A226370 A226371 A226372
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KEYWORD
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nonn,easy
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AUTHOR
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Alois P. Heinz, Jun 05 2013
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STATUS
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approved
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