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A278330
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Number of tilings of a 5 X n rectangle using n pentominoes of shapes P, U, X.
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6
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1, 0, 2, 1, 12, 10, 59, 52, 276, 349, 1404, 1984, 7019, 11148, 35686, 62181, 182776, 339350, 942507, 1841208, 4887096, 9921685, 25442304, 53190380, 132928715, 284198328, 696276202, 1514363221, 3654567764, 8053235650, 19212546163, 42762014028, 101125071372
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,2,2,8,4,21,-8,-4,-6,0,-16,-8).
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FORMULA
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G.f.: -(4*x^6+x^3-1) / (8*x^12 +16*x^11 +6*x^9 +4*x^8 +8*x^7 -21*x^6 -4*x^5 -8*x^4 -2*x^3 -2*x^2+1).
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EXAMPLE
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a(2) = 2, a(3) = 1:
.___. .___. ._____.
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| ._| |_. | |_| |_|
|_| | | |_| |_ _|
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|___| |___| |_____| .
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MAPLE
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a:= n-> (Matrix(12, (i, j)-> `if`(i+1=j, 1, `if`(i=12,
[-8, -16, 0, -6, -4, -8, 21, 4, 8, 2, 2, 0][j], 0)))^n.
<<1, 0, 2, 1, 12, 10, 59, 52, 276, 349, 1404, 1984>>)[1, 1]:
seq(a(n), n=0..35);
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CROSSREFS
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Cf. A079978, A174249, A233427, A234312, A234931, A247124, A247268, A247443, A249762, A264765, A264812.
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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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