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A042301
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Denominators of continued fraction convergents to sqrt(677).
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3
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1, 52, 2705, 140712, 7319729, 380766620, 19807183969, 1030354333008, 53598232500385, 2788138444353028, 145036797338857841, 7544701600064960760, 392469520000716817361, 20415959741637339463532, 1062022376085142368921025, 55245579516169040523356832
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OFFSET
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0,2
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COMMENTS
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Also called the 52-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 52 kinds of squares available. (End)
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LINKS
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FORMULA
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a(n) = F(n, 52), the n-th Fibonacci polynomial evaluated at x=52. - T. D. Noe, Jan 19 2006
a(n) = 52*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=52.
G.f.: 1/(1 - 52*x - x^2). (End)
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MATHEMATICA
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LinearRecurrence[{52, 1}, {1, 52}, 20] (* Harvey P. Dale, Mar 24 2023 *)
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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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