[seqfan] Re: Proof and formulas wanted for A247239

Benoît Jubin benoit.jubin at gmail.com
Mon Dec 1 13:48:33 CET 2014


I think it is proved in the link in that sequence to
http://www.les-mathematiques.net
I'm refering to the matrix solution given there by Guego and
MathMPA2013: there is an obvious closed form for A^{-1}, so we can see
that it has integer coefficients, and the sums in A247239 are of the
form trace(A{-m}) so are integers. You can have a look at the
wikipedia entry for tridiagonal matrices.
Benoît

On Mon, Dec 1, 2014 at 12:03 PM, Jean-François Alcover
<jf.alcover at gmail.com> wrote:
>  Dear SeqFans,
>
> A proof that all terms of A247239 <http://oeis.org/A247239> are integers is
> wanted.
> (such a proof exceeds my capability!)
>
> It would also be interesting to get a general nontrig formula.
> I noticed that rows could be computed as linear recurrences.
> Example: a(5,m) = 19*a(5,m-1) - 96*a(5,m-2) + 144*a(5,m-3),
> with g.f. = (5 - 60*x + 144*x^2)/(1 - 19*x + 96*x^2 - 144*x^3),
> giving the explicit formula a(5,m) = 2^(2n+1) + 3^n + 2^(2n+1)*3^n.
>
> I couldn't  find a general explicit or recurrence formula, or g.f.
> Hope an expert will be able to find it...
>
> Jean-François
>
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