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A270062
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Number of tilings of a 2 X n rectangle using monominoes and trominoes of any shape.
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2
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1, 1, 5, 14, 45, 140, 438, 1371, 4287, 13413, 41956, 131249, 410572, 1284352, 4017713, 12568213, 39315905, 122988066, 384731445, 1203517448, 3764844982, 11777193395, 36841433019, 115247422841, 360517151000, 1127770261265, 3527892525112, 11035958382864
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: -(x^3+x^2-1)/(x^6+x^5-x^4-5*x^3-5*x^2-x+1).
a(n) = a(n-1) +5*(a(n-2)+a(n-3)) +a(n-4) -a(n-5) -a(n-6).
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EXAMPLE
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a(3) = 14:
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_____| |_|_|_| |_____| |_| |_| | |_|_| | ._|_| |_. |_|
|_____| |_____| |_|_|_| |___|_| |___|_| |_|_|_| |_|_|_|
.
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_|_|_| | ._| | | |_. | |_|_| | |_| |_| |_| ._| |_|_. |
|_|_|_| |_|___| |___|_| |_|___| |_|___| |_|_|_| |_|_|_| .
.
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MAPLE
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a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1, `if`(i=6, [-1$2, 1,
5$2, 1][j], 0)))^n. <<1, 1, 5, 14, 45, 140>>)[1, 1]:
seq(a(n), n=0..30);
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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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