[seqfan] Re: A160242

Paolo Lava paoloplava at gmail.com
Fri Apr 16 08:02:33 CEST 2010


Ok, thanks Maximilian!

Paolo

2010/4/15 Maximilian Hasler <maximilian.hasler at gmail.com>

> On Thu, Apr 15, 2010 at 10:36 AM, Paolo Lava <paoloplava at gmail.com> wrote:
> > Hi Seqfans,
> >
> > It could be that the original definition of A160242 (see comment) was
> right
> > but I certainly do not understand the present one. It should be like
> A010052
>
>
> That's very confusing, because one cannot know who made what change.
> (All comments not in the original submission should be signed and
> dated, but here none of them are.
> The latest update I have in my mailbox is from Richard Mathar, Dec 08
> 2009, and seems reasonable, but no trace of it seems in OEIS.
> I include it below, I think Neil should replace the current version by this
> one
> In case of doubt, I vote for deletion. As someone else put it:
>
> On Sat, Dec 12, 2009 at 7:52 AM, Joerg Arndt <arndt at jjj.de> wrote:
> > The whole think is stinky on many levels.
>
> Maximilian
>
>
> On Tue, Dec 8, 2009 at 1:38 PM, Richard Mathar
> <mathar at strw.leidenuniv.nl> wrote:
> >
> > From the OEIS point of view, I've basically reduced all the
> Boubaker-related
> > Ghanouchi submissions (A131386 etc, search for "Ghanouchi") to their
> > polynomial definition (which is easy...). And the screaming (and
> wrong...)
> > title in the %H line of the Oyodum article in A160242 has of course to be
> > corrected; in particular this is now an URL (not a PDF) to the original
> > article which has a link (!) to the article this one comments to.
> Apparently
> > they want to avoid that somone gets easily to the original article.
> >
> > I've submitted the following to Neil:
>
>
> %I A160242
> %S A160242
> 1,2,1,2,2,2,1,2,2,2,2,2,1,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,1,2,2,2,2,
> %T A160242
> 2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,
> %U A160242
> 2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2
> %N A160242 Triangle A(n,m) read by rows: a quarter of the Fourier
> coefficient [cos(m*t)] of the shifted Boubaker polynomial B_n(2*cos
> t)-2*cos(n*t).
> %C A160242 Starting from the polynomials B_n(x) defined in A137276 and
> A135929, we insert x=2*cos(t),
> %C A160242 and define the Fourier coefficients A(n,m) by B_n(2*cos
> t)-2*cos(n*t) = 4*sum(m=0,..,n-2) A(n,m)*cos(m*t).
> %C A160242 A(n,m) is not an integer for n=0, so the table starts at
> n=1. Furthermore, A(n,m)=0 if n-m is odd, these
> %C A160242 regular zeros are skipped as usual, so effectively the
> first table entry appears at n=2.
> %H A160242 A. Luzon and M. A. Morson, <a
> href="http://arxiv.org/abs/0904.2672">Recurrence relations for
> polynomial sequences via Riordan matrices</a>, arXiv:0904.2672
> [math.CO]
> %H A160242 O. D. Oyodum, O. B. Awojoyogbe, M. Dada and J. Magnuson, <a
> href="http://dx.doi.org/10.1051/epjap/2009036">Comment on "Enhancement
> of pyrolysis spray disposal .. deposition"</a>, Eur. Phys. J. - Appl.
> Phys., EPJAP, 46 (2009), 21201.
> %e A160242 Using T^m =cos(m*t) as a notational shortcut, the expansions
> start
> %e A160242 ; B_1(2 cos t)-2*cos 1 t = 0
> %e A160242 1 ; B_2(2 cos t)-2*cos 2 t = 1
> %e A160242 0 2 ; B_3(2 cos t)-2*cos 3 t = 2*T
> %e A160242 1 0 2 ; B_4(2 cos t)-2*cos 4 t = 1+2*T^2
> %e A160242 0 2 0 2 ; B_5(2 cos t)-2*cos 5 t = 2*T+2*T^3
> %e A160242 1 0 2 0 2 ; B_6(2 cos t)-2*cos 6 t = 1+2*T^2+2*T^4
> %e A160242 0 2 0 2 0 2 ; B_7(2 cos t)-2*cos 7 t = 2*T+2*T^3+2*T^5
> %e A160242 1 0 2 0 2 0 2 ; B_8(2 cos t)-2*cos 8 t = 1+2*T^2+2*T^4+2*T^6
> %e A160242 0 2 0 2 0 2 0 2 ; B_9(2 cos t)-2*cos 9 t = 2*T+2*T^3+2*T^5+2*T^7
> %e A160242 1 0 2 0 2 0 2 0 2 ; B_10(2 cos t)-2*cos 10 t =
> 1+2*T^2+2*T^4+2*T^6+2*T^8
> %e A160242 0 2 0 2 0 2 0 2 0 2 ; B_11(2 cos t)-2*cos 11 t =
> 2*T^3+2*T^5+2*T^7+2*T^9+2*T
> %K A160242 nonn,tabl
> %O A160242 2,2
> %A A160242 Haidar Rahmanov (hrahmanov(AT)yahoo.com.au), May 05 2009
> %E A160242 Definition clarified, publication title corrected, sequence
> extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 07 2009
>
>
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