Search: id:A087281
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%I A087281
%S A087281 2,29,843,24476,710647,20633239,599074578,17393796001,505019158607,
%T A087281 14662949395604,425730551631123,12360848946698171,358890350005878082,
%U A087281 10420180999117162549,302544139324403592003,8784200221406821330636
%N A087281 Lucas numbers L(7n).
%C A087281 a(n+1)/a(n) converges to (29+sqrt(845))/2 = 29.0344418537... a(0)/a(1)=2/
               29; a(1)/a(2)=29/843; a(2)/a(3)=843/24476; a(3)/a(4)=24476/710647; 
               ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.0344418537... 
               = 2/(29+sqrt(845)) = (sqrt(845)-29)/2.
%H A087281 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A087281 <a href="Sindx_Rea.html#recur1">Index entries for recurrences a(n) = 
               k*a(n - 1) +/- a(n - 2)</a>
%F A087281 a(n) =29a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 29, a(n) = 
               ((29+sqrt(845))/2)^n + ((29-sqrt(845))/2)^n, (a(n))^2 =a(2n)-2 if 
               n=1, 3, 5..., (a(n))^2 =a(2n)+2 if n=2, 4, 6....
%F A087281 G.f.: (2-29*x)/(1-29*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 02 2008]
%e A087281 a(4) = 710647 = 29a(3) + a(2) = 29*24476+ 843=((29+sqrt(845))/2)^4 + 
               ( (29-sqrt(845))/2)^4 =710646.9999985928 + 0.0000014071 = 710647.
%Y A087281 Cf. A000032.
%Y A087281 Sequence in context: A013517 A006988 A090251 this_sequence A024234 A077282 
               A059725
%Y A087281 Adjacent sequences: A087278 A087279 A087280 this_sequence A087282 A087283 
               A087284
%K A087281 easy,nonn
%O A087281 0,1
%A A087281 Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003
%E A087281 More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 
               2004

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