[seqfan] Re: A087035 (convolution of permutations) and A213387 (count of triples)
David Applegate
david at research.att.com
Tue Jun 26 18:14:55 CEST 2012
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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