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A041925
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Denominators of continued fraction convergents to sqrt(485).
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3
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1, 44, 1937, 85272, 3753905, 165257092, 7275065953, 320268159024, 14099074063009, 620679526931420, 27323998259045489, 1202876602924932936, 52953894526956094673, 2331174235788993098548, 102624620269242652430785, 4517814466082465700053088
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OFFSET
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0,2
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COMMENTS
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Also called the 44-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 44 kinds of squares available. (End)
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LINKS
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FORMULA
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a(n) = F(n, 44), the n-th Fibonacci polynomial evaluated at x=44. - T. D. Noe, Jan 19 2006
a(n) = 44*a(n-1) + a(n-2) for n>1; a(0)=1, a(1)=44.
G.f.: 1/(1-44*x-x^2). (End)
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MATHEMATICA
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Denominator[Convergents[Sqrt[485], 20]] (* Harvey P. Dale, Oct 20 2011 *)
CoefficientList[Series[1/(1 - 44 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 27 2013 *)
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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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