Search: id:A088316
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%I A088316
%S A088316 2,13,171,2236,29239,382343,4999698,65378417,854919119,11179326964,
%T A088316 146186169651,1911599532427,24996980091202,326872340718053,
%U A088316 4274337409425891,55893258663254636,730886700031736159
%N A088316 a(n) = 13a(n-1) + a(n-2).
%C A088316 a(n+1)/a(n) converges to (13+sqrt(173))/2 = 13.07647321... a(0)/a(1)=2/
               13; a(1)/a(2)=13/171; a(2)/a(3)=171/2236; a(3)/a(4)= 2236/29239; 
               ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.07647321... 
               = 2/(13+sqrt(173)) = (sqrt(173)-13)/2.
%H A088316 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A088316 <a href="Sindx_Rea.html#recur1">Index entries for recurrences a(n) = 
               k*a(n - 1) +/- a(n - 2)</a>
%F A088316 a(n) = 13a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 13. a(n) 
               = [(13+sqrt(173))/2]^n + [(13-sqrt(173))/2]^n.
%F A088316 G.f.: (2-13*x)/(1-13*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 02 2008]
%e A088316 a(4) = 29239 = 13a(3) + a(2) = 13*2236 + 171 = [(13+sqrt(173))/2]^4 + 
               [(13-sqrt(173))/2]^4 = 29238.9999657 + 0.0000342 =29239.
%Y A088316 Cf. A006905.
%Y A088316 Sequence in context: A132521 A078363 A143851 this_sequence A006905 A119400 
               A137610
%Y A088316 Adjacent sequences: A088313 A088314 A088315 this_sequence A088317 A088318 
               A088319
%K A088316 easy,nonn
%O A088316 0,1
%A A088316 Nikolay V. Kosinov, Dmitry V. Polyakov (kosinov(AT)unitron.com.ua), Nov 
               06 2003

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