Search: id:A086594
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%I A086594
%S A086594 2,8,66,536,4354,35368,287298,2333752,18957314,153992264,1250895426,
%T A086594 10161155672,82540140802,670482282088,5446398397506,44241669462136,
%U A086594 359379754094594,2919279702218888
%N A086594 a(n)=8a(n-1)+a(n-2), starting with a(0)=2 and a(1)=8.
%C A086594 Harmonious sequence, build on the number 8.1231056...
%C A086594 a(n+1)/a(n) converges to 4+sqrt(17). a(0)/a(1)=1/4; a(1)/a(2)=8/66; a(2)/
               a(3)=66/536; a(3)/a(4)=536/4354;...etc. Lim a(n)/a(n+1)as n approaches 
               infinity=0.123105625...=1/(4+sqrt(17))=sqrt(17)-4.
%H A086594 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A086594 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A086594 <a href="Sindx_Rea.html#recur1">Index entries for recurrences a(n) = 
               k*a(n - 1) +/- a(n - 2)</a>
%F A086594 a(n)=(4+sqrt(17))^n+(4-sqrt(17))^n.
%F A086594 O.g.f: 2*(-1+4*x)/(-1+8*x+x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Dec 02 2007
%e A086594 a(4)=4354=8a(3)+a(2)=8*536+66=(4+sqrt(17))^4+(4-sqrt(17))^4=4353.9997703+
%e A086594 0.0002297=4354.
%Y A086594 Cf. A003285.
%Y A086594 Sequence in context: A009602 A011836 A100623 this_sequence A132219 A023164 
               A053922
%Y A086594 Adjacent sequences: A086591 A086592 A086593 this_sequence A086595 A086596 
               A086597
%K A086594 easy,nonn
%O A086594 0,1
%A A086594 Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 11 2003

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