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%I #35 Sep 08 2022 08:45:11
%S 2,8,66,536,4354,35368,287298,2333752,18957314,153992264,1250895426,
%T 10161155672,82540140802,670482282088,5446398397506,44241669462136,
%U 359379754094594,2919279702218888,23713617371845698,192628218676984472,1564739366787721474
%N a(n) = 8*a(n-1) + a(n-2), starting with a(0)=2 and a(1)=8.
%C a(n+1)/a(n) converges to 4 + sqrt(17).
%H Vincenzo Librandi, <a href="/A086594/b086594.txt">Table of n, a(n) for n = 0..1000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rea#recur1">Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,1).
%F a(n) = (4+sqrt(17))^n + (4-sqrt(17))^n.
%F O.g.f: 2*(-1+4*x)/(-1+8*x+x^2). - _R. J. Mathar_, Dec 02 2007
%F a(n) = 2*A088317(n). - _R. J. Mathar_, Sep 27 2014
%e a(4) = 8*a(3)+a(2) = 8*536+66 = 4354.
%t LinearRecurrence[{8,1},{2,8},30] (* _Harvey P. Dale_, Sep 21 2014 *)
%t RecurrenceTable[{a[0] == 2, a[1] == 8, a[n] == 8 a[n-1] + a[n-2]}, a, {n, 30}] (* _Vincenzo Librandi_, Sep 19 2016 *)
%o (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
%o (PARI) x='x+O('x^30); Vec(2*(1-4*x)/(1-8*x-x^2)) \\ _G. C. Greubel_, Nov 07 2018
%Y Cf. A003285.
%K nonn,easy
%O 0,1
%A Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 11 2003
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