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A087798
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a(n) = 9*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 9.
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18
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2, 9, 83, 756, 6887, 62739, 571538, 5206581, 47430767, 432083484, 3936182123, 35857722591, 326655685442, 2975758891569, 27108485709563, 246952130277636, 2249677658208287, 20494051054152219, 186696137145578258
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OFFSET
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0,1
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COMMENTS
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a(n+1)/a(n) converges to (9 + sqrt(85))/2.
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LINKS
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FORMULA
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a(n) = ((9 + sqrt(85))/2)^n + ((9 - sqrt(85))/2)^n.
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EXAMPLE
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a(4) = 9*a(3) + a(2) = 9*756 + 83 = 6887.
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MATHEMATICA
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RecurrenceTable[{a[0] == 2, a[1] == 9, a[n] == 9 a[n-1] + a[n-2]}, a, {n, 30}] (* Vincenzo Librandi, Sep 19 2016 *)
LinearRecurrence[{9, 1}, {2, 9}, 30] (* G. C. Greubel, Nov 07 2018 *)
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PROG
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(Magma) I:=[2, 9]; [n le 2 select I[n] else 9*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 19 2016
(PARI) x='x+O('x^30); Vec((2-9*x)/(1-9*x-x^2)) \\ G. C. Greubel, Nov 07 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Nikolay V. Kosinov, Dmitry V. Poljakov (kosinov(AT)unitron.com.ua), Oct 10 2003
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EXTENSIONS
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STATUS
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approved
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