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A086594
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a(n) = 8*a(n-1) + a(n-2), starting with a(0)=2 and a(1)=8.
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18
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2, 8, 66, 536, 4354, 35368, 287298, 2333752, 18957314, 153992264, 1250895426, 10161155672, 82540140802, 670482282088, 5446398397506, 44241669462136, 359379754094594, 2919279702218888, 23713617371845698, 192628218676984472, 1564739366787721474
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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 4 + sqrt(17).
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LINKS
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FORMULA
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a(n) = (4+sqrt(17))^n + (4-sqrt(17))^n.
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EXAMPLE
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a(4) = 8*a(3)+a(2) = 8*536+66 = 4354.
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MATHEMATICA
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LinearRecurrence[{8, 1}, {2, 8}, 30] (* Harvey P. Dale, Sep 21 2014 *)
RecurrenceTable[{a[0] == 2, a[1] == 8, a[n] == 8 a[n-1] + a[n-2]}, a, {n, 30}] (* Vincenzo Librandi, Sep 19 2016 *)
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PROG
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(Magma) I:=[2, 8]; [n le 2 select I[n] else 8*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 19 2016
(PARI) x='x+O('x^30); Vec(2*(1-4*x)/(1-8*x-x^2)) \\ G. C. Greubel, Nov 07 2018
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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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Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 11 2003
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STATUS
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approved
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