%I A087619
%S A087619 2,137,18771,2571764,352350439,48274581907,6613970071698,
%T A087619 906162174404533,124150831863492719,17009570127472907036,
%U A087619 2330435258295651756651,319286639956631763568223
%N A087619 a(n) = 137a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 137.
%C A087619 a(n+1)/a(n) converges to (137+sqrt(18773))/2 = 137.00729888121410965... 
               a(0)/a(1) = 2/137; a(1)/a(2) = 137/18771; a(2)/a(3) = 18771/2571764; 
               a(3)/a(4) = 2571764/352350439; ... etc. Lim a(n)/a(n+1) as n approaches 
               infinity = 0.00729888121410965... = 2/(137+sqrt(18773)) = (sqrt(18773)-137)/
               2.
%H A087619 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A087619 a(n) =137a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 137, a(n) 
               = ((137+sqrt(18773))/2)^n + ((137-sqrt(18773))/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 A087619 G.f.: (2-137*x)/(1-137*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 23 2008]
%e A087619 a(4) = 352350439 = 137a(3) + a(2) = 137*2571764+ 18771 = ((137+sqrt(18773))/
               2)^4 + ( (137-sqrt(18773))/2)^4 = 352350438.999999997161916 + 0.000000002838083 
               = 352350439.
%Y A087619 Cf. A037088, A073481.
%Y A087619 Sequence in context: A065963 A000662 A139907 this_sequence A157072 A051029 
               A084560
%Y A087619 Adjacent sequences: A087616 A087617 A087618 this_sequence A087620 A087621 
               A087622
%K A087619 easy,nonn
%O A087619 0,1
%A A087619 Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 25 2003