[seqfan] Asymptotic formula

[CLOITRE Benoit]

<div>Dear seqfans,<br /><br />I came across this sequence defined by the recursion:<br /><br />a(1)=1, a(2)=1, n>=3, a(n)=r*(a(ceil(n/2))-a(floor(n/2))) where r>1.<br /><br />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 reference for the general case or confirm this fact for r=2 and r=3/2?<br /><br />Thanks<br />BC<br /></div><br />