[seqfan] Re: A160242
Maximilian Hasler
maximilian.hasler at gmail.com
Thu Apr 15 10:55:05 CEST 2010
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
More information about the SeqFan
mailing list