[seqfan] Re: Asymptotic formula

Olivier Gerard olivier.gerard at gmail.com
Sat Apr 30 10:10:38 CEST 2011

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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?


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