[seqfan] Re: A087035 (convolution of permutations) and A213387 (count of triples)
Max Alekseyev
maxale at gmail.com
Wed Jun 27 11:46:36 CEST 2012
I've merged these sequence as A087035.
Max
On Tue, Jun 26, 2012 at 8:14 PM, David Applegate <david at research.att.com> wrote:
> Yes.
>
> A simple local maximization argument for A087035 shows that
>
> if n is odd, A087035(n) = n^2 + A087035(n-1)
> if n is even, A087035(n) = 2*n*(n-1) + A087035(n-2)
>
> (if n is odd, the sum is maximized by setting p((n+1)/2)=n,
> contributing n^2 to the sum, and if n is even, the sum is maximized by
> setting, say, p(1)=n, p(n)=(n-1)).
>
> This recurrence is also satisfied by the formula given for A213387:
>
> a(n) = (2*n*(n+2)*(2*n+5)+3*(-1)^n+9)/12
>
> (for a(n+1))
>
> -Dave
>
>> From seqfan-bounces at list.seqfan.eu Tue Jun 26 09:33:17 2012
>> From: Richard Mathar <mathar at strw.leidenuniv.nl>
>> Date: Tue, 26 Jun 2012 15:32:56 +0200
>> To: seqfan at seqfan.eu
>> Subject: [seqfan] A087035 (convolution of permutations) and A213387 (count of triples)
>
>> Is there some reason why http://oeis.org/A087035 and http://oeis.org/A213387
>> might be the same (up to a shift in the index)?
>
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>
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