[seqfan] Re: [ Re: Asymptotic formula]

CLOITRE Benoit benoit7848c at orange.fr
Sat Apr 30 11:01:34 CEST 2011


I think there's something wrong here. As written, a(n) = 0 for any even <BR>n > 2. Is this really what is intended?<BR><BR>Franklin T. Adams-Watters<BR><BR>-----Original Message-----<BR>From: Olivier Gerard <olivier.gerard at gmail.com><BR><BR>Benoit's message has suffered a transmission problem,<BR>Here is a more legible version:<BR>==============================================<BR><BR>Dear seqfans,<BR><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 <BR>guess<BR>u(n)<<n if r=2 and u(n)<<n^(1/2)L(n) if r=3/2 where L is a slowly <BR>varying<BR>function. Does anyone know a reference for the general case or confirm <BR>this<BR>fact for r=2 and r=3/2?<BR><BR>Thanks<BR>BC<BR><BR>_______________________________________________<BR><BR>Seqfan Mailing list - http://list.seqfan.eu/<BR>


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