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A041313
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Denominators of continued fraction convergents to sqrt(170).
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3
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1, 26, 677, 17628, 459005, 11951758, 311204713, 8103274296, 210996336409, 5494008020930, 143055204880589, 3724929334916244, 96991217912702933, 2525496595065192502, 65759902689607707985, 1712282966524865600112, 44585117032336113310897
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OFFSET
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0,2
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COMMENTS
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Also called the 26-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 26 kinds of squares available. (End)
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LINKS
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FORMULA
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a(n) = F(n, 26), the n-th Fibonacci polynomial evaluated at x=26. - T. D. Noe, Jan 19 2006
a(n) = 26*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=26.
G.f.: 1/(1-26*x-x^2). (End)
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MATHEMATICA
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LinearRecurrence[{26, 1}, {1, 26}, 20] (* Harvey P. Dale, Jul 26 2017 *)
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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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