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A042513
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Denominators of continued fraction convergents to sqrt(785).
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3
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1, 56, 3137, 175728, 9843905, 551434408, 30890170753, 1730400996576, 96933345979009, 5429997775821080, 304176808791959489, 17039331290125552464, 954506729055822897473, 53469416158416207810952, 2995241811600363460310785, 167787010865778769985214912
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OFFSET
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0,2
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COMMENTS
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Also called the 56-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
a(n) is the number of tilings of an n-board (a board with dimensions n X 1) using unit squares and dominoes (with dimensions 2 X 1) if there are 56 kinds of squares available. (End)
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LINKS
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FORMULA
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a(n) = F(n, 56), the n-th Fibonacci polynomial evaluated at x=56. - T. D. Noe, Jan 19 2006
a(n) = 56*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=56.
G.f.: 1/(1 - 56*x - x^2). (End)
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MATHEMATICA
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Denominator[Convergents[Sqrt[785], 30]] (* Harvey P. Dale, Jun 26 2012 *)
CoefficientList[Series[1/(1 - 56 x - x^2), {x, 0, 25}], x] (* Vincenzo Librandi, Jan 23 2014 *)
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CROSSREFS
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KEYWORD
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nonn,frac,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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