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A015584
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Expansion of g.f. x/(1 - 9*x - 8*x^2).
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3
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0, 1, 9, 89, 873, 8569, 84105, 825497, 8102313, 79524793, 780541641, 7661073113, 75193991145, 738034505209, 7243862476041, 71099038326041, 697842244742697, 6849372509292601, 67227090541574985, 659838794948515673, 6476365878869240937, 63566003269411293817
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OFFSET
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0,3
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COMMENTS
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Pisano period lengths: 1, 1, 4, 1, 24, 4, 6, 1, 4, 24, 10, 4, 12, 6, 24, 1,144, 4, 15, 24, ... . - R. J. Mathar, Aug 10 2012
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LINKS
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FORMULA
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a(n) = 9*a(n-1) + 8*a(n-2).
a(n) = (-((9-sqrt(113))/2)^n + ((9+sqrt(113))/2)^n) / sqrt(113). - Colin Barker, May 16 2017
E.g.f.: 2*exp(9*x/2)*sinh(sqrt(113)*x/2)/sqrt(113). - Stefano Spezia, Oct 25 2023
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MATHEMATICA
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CoefficientList[Series[x/(1-9x-8x^2), {x, 0, 30}], x] (* Harvey P. Dale, Sep 06 2022 *)
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PROG
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(Sage) [lucas_number1(n, 9, -8) for n in range(0, 19)] # Zerinvary Lajos, Apr 26 2009
(Magma) [n le 2 select n-1 else 9*Self(n-1) + 8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2012
(PARI) concat(0, Vec(x / (1-9*x-8*x^2) + O(x^30))) \\ Colin Barker, May 16 2017
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CROSSREFS
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KEYWORD
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nonn,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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