A136010 solved

[zak seidov]

And in general, at recurrency
a[n]==A a[n-1]+B a[n-2], (A>0)
 
lim (n->+inf) a(n+1)/a(n)=
(A+sqrt(A^2+4B))/2.

--- franktaw at netscape.net wrote:

> See below for the answer.
> 
> Franklin T. Adams-Watters
> 
> -----Original Message-----
> From: Don Reble <djr at nk.ca>
> 
> Seqfans, njas, Jordan:
> 
> > %I A136010
> > %S A136010 
>
20,9,243,1782,14661,118665,962604,7806213,63306927,513404406
> > %N A136010 From an online IQ test (Adaptive IQ ).
> Solution not known
> >            to the submitter.
> 
>     a(1)=20, a(2)=9, a(n+2) = 7*a(n+1) + 9*a(n).
> 
>     Quick puzzle: What's lim (n->+inf) a(n+1)/a(n) ?
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> That would be the larger root of x^2-7x-9, which is
> (7+sqrt(85))/2, or 
> 8.1097722286464436550011371408814....
> 



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