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A041145
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Denominators of continued fraction convergents to sqrt(82).
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9
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1, 18, 325, 5868, 105949, 1912950, 34539049, 623615832, 11259624025, 203296848282, 3670602893101, 66274148924100, 1196605283526901, 21605169252408318, 390089651826876625, 7043218902136187568
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OFFSET
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0,2
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COMMENTS
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For n >= 2, a(n) equals the permanent of the (n-1) X (n-1) tridiagonal matrix with 18's along the main diagonal, and 1's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 08 2011
a(n) equals the number of words of length n on alphabet {0,1,...,18} avoiding runs of zeros of odd lengths. - Milan Janjic, Jan 28 2015
Also called the 18-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 18 kinds of squares available. (End)
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LINKS
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FORMULA
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a(n) = F(n,18), the n-th Fibonacci polynomial evaluated at x=18. - T. D. Noe, Jan 19 2006
a(n) = 18*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=18.
G.f.: 1/(1 - 18*x - x^2). (End)
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MATHEMATICA
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CROSSREFS
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Cf. similar sequences listed in A243399.
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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