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A042405
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Denominators of continued fraction convergents to sqrt(730).
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3
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1, 54, 2917, 157572, 8511805, 459795042, 24837444073, 1341681774984, 72475653293209, 3915026959608270, 211483931472139789, 11424047326455156876, 617110039560050611093, 33335366183569188155898, 1800726883952296211029585, 97272587099607564583753488
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OFFSET
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0,2
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COMMENTS
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Also called the 54-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 54 kinds of squares available. (End)
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LINKS
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FORMULA
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a(n) = F(n, 54), the n-th Fibonacci polynomial evaluated at x=54. - T. D. Noe, Jan 19 2006
a(n) = 54*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=54.
G.f.: 1/(1 - 54*x - x^2). (End)
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MATHEMATICA
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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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