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A041421
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Denominators of continued fraction convergents to sqrt(226).
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3
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1, 30, 901, 27060, 812701, 24408090, 733055401, 22016070120, 661215159001, 19858470840150, 596415340363501, 17912318681745180, 537965975792718901, 16156891592463312210, 485244713749692085201, 14573498304083225868240
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OFFSET
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0,2
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COMMENTS
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Also called the 30-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 30 kinds of squares available. (End)
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LINKS
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FORMULA
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a(n) = F(n, 30), the n-th Fibonacci polynomial evaluated at x=30. - T. D. Noe, Jan 19 2006
a(n) = 30*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=30.
G.f.: 1/(1-30*x-x^2). (End)
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MATHEMATICA
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LinearRecurrence[{30, 1}, {1, 30}, 20] (* Harvey P. Dale, Jun 30 2022 *)
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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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