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A042625
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Denominators of continued fraction convergents to sqrt(842).
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3
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1, 58, 3365, 195228, 11326589, 657137390, 38125295209, 2211924259512, 128329732346905, 7445336400380002, 431957840954387021, 25061000111754827220, 1453969964322734365781, 84355318930830348042518, 4894062467952482920831825, 283939978460174839756288368
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OFFSET
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0,2
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COMMENTS
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Also called the 58-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 58 kinds of squares available. (End)
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LINKS
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FORMULA
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a(n) = F(n, 58), the n-th Fibonacci polynomial evaluated at x=58. - T. D. Noe, Jan 19 2006
a(n) = 58*a(n-1) + a(n-2) for n>1; a(0)=1, a(1)=58.
G.f.: 1/(1 - 58*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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