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A364460
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Number of tilings of a 3 X n rectangle using dominoes and trominoes (of any shape).
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2
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1, 1, 6, 30, 145, 733, 3540, 17300, 84479, 411963, 2011408, 9816506, 47911847, 233851991, 1141365064, 5570761346, 27189615925, 132706261547, 647709321582, 3161321546320, 15429691961077, 75308819284819, 367565220881250, 1794002281279416, 8756117243124305
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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 (3,6,13,0,53,18,69,48,35,-125,-76,-24,38,8,18,1,-3,-1).
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FORMULA
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G.f.: -(x^15 +2*x^14 +4*x^13 -5*x^12 -9*x^11 -18*x^10 +16*x^9 +5*x^8 +8*x^7 -10*x^6 +13*x^5 -6*x^4 +7*x^3 +3*x^2 +2*x -1) / (x^18 +3*x^17 -x^16 -18*x^15 -8*x^14 -38*x^13 +24*x^12 +76*x^11 +125*x^10 -35*x^9 -48*x^8 -69*x^7 -18*x^6 -53*x^5 -13*x^3 -6*x^2 -3*x +1).
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EXAMPLE
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a(2) = 6:
.___. .___. .___. .___. .___. .___.
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|_|_| |___| |___| |_|_| |___| |___| .
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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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