[seqfan] Re: Asymptotic formula

[franktaw at netscape.net]

I think there's something wrong here. As written, a(n) = 0 for any even 
n > 2. Is this really what is intended?

Franklin T. Adams-Watters

-----Original Message-----
From: Olivier Gerard <olivier.gerard at gmail.com>

Benoit's message has suffered a transmission problem,
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==============================================

Dear seqfans,


I came across this sequence defined by the recursion:

a(1)=1, a(2)=1, n>=3, a(n)=r*(a(ceil(n/2))-a(floor(n/2))) where r>1.

I'm interested with the asymptotic behaviour of a(n). For instance I 
guess
u(n)<<n if r=2 and u(n)<<n^(1/2)L(n) if r=3/2 where L is a slowly 
varying
function. Does anyone know a reference for the general case or confirm 
this
fact for r=2 and r=3/2?

Thanks
BC