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A253265
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The number of tilings of 2 X n boards with squares of 2 colors and dominoes of 3 colors.
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2
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1, 7, 82, 877, 9565, 103960, 1130701, 12296275, 133724242, 1454268793, 15815379409, 171994465072, 1870463946217, 20341557798991, 221217294787570, 2405769114915733, 26163076626035413, 284527128680078536, 3094272440210485525, 33650646877362841531, 365955505581792121138
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OFFSET
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0,2
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COMMENTS
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The numerator in Formula (3) in the JIS article should be 1-b*x, not 1-x.
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LINKS
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FORMULA
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G.f.: ( 1-3*x ) / ( 1 - 10*x - 12*x^2 + 27*x^3 ).
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MAPLE
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seq(coeff(series((1-3*x)/(1-10*x-12*x^2+27*x^3), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 28 2019
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MATHEMATICA
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CoefficientList[Series[(1-3x)/(1-10x-12x^2+27x^3), {x, 0, 20}], x] (* Michael De Vlieger, Sep 30 2015 *)
LinearRecurrence[{10, 12, -27}, {1, 7, 82}, 30] (* Harvey P. Dale, Dec 30 2015 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((1-3*x)/(1-10*x-12*x^2+27*x^3)) \\ G. C. Greubel, Oct 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-3*x)/(1-10*x-12*x^2+27*x^3) )); // G. C. Greubel, Oct 28 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-3*x)/(1-10*x-12*x^2+27*x^3)).list()
(GAP) a:=[1, 7, 82];; for n in [4..30] do a[n]:=10*a[n-1]+12*a[n-2] -27*a[n-3]; od; a; # G. C. Greubel, Oct 28 2019
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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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