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A233036
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The maximum number of I-tetrominoes that can be packed into an n X n array of squares when rotation is allowed.
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4
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0, 0, 0, 4, 6, 8, 12, 16, 20, 24, 30, 36, 42, 48, 56, 64, 72, 80, 90, 100, 110, 120, 132, 144, 156, 168, 182, 196, 210, 224, 240, 256, 272, 288, 306, 324, 342, 360, 380, 400, 420, 440, 462, 484, 506, 528, 552, 576, 600, 624, 650, 676, 702, 728, 756, 784, 812, 840, 870, 900, 930, 960, 992, 1024, 1056
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OFFSET
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1,4
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COMMENTS
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By de Bruijn's theorem (see the de Bruijn link), an m X n rectangle can't be tiled with I tetrominoes unless m or n is divisible by 4. - Robert Israel, Oct 15 2015
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LINKS
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FORMULA
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a(4*k) = 4*k^2.
a(2*k+1) = k*(k+1) for k >= 2.
a(4*k+2) = 4*k*(k+1).
G.f.: 2*x^3/((1 + x)*(1 + x^2)*(1 - x)^3) - 2*x^3. (End)
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MAPLE
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0$3, seq(op([4*k^2, 2*k*(2*k+1), 4*k*(k+1), (2*k+1)*(2*k+2)]), k=1..20); # Robert Israel, Oct 15 2015
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MATHEMATICA
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CoefficientList[Series[2 x^3/((1 + x) (1 + x^2) (1 - x)^3) - 2 x^3, {x, 0, 100}], x] (* Vincenzo Librandi, Oct 15 2015 *)
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {0, 0, 0, 4, 6, 8, 12, 16, 20}, 70] (* Harvey P. Dale, Dec 16 2018 *)
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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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EXTENSIONS
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STATUS
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approved
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