[seqfan] Re: OEIS wiki and editing, Boubaker affair.

[Richard Mathar]

Hooking up to
http://list.seqfan.eu/pipermail/seqfan/2009-December/003143.html

ak> About Boubaker-polynomials: I don't think there's nothing about sequences
ak> like
ak> http://www.research.att.com/~njas/sequences/A162180
ak> why they wouldn't be allowed into OEIS. People submit

my question is: If I use the definition and recurrence in A162180,
the polynomials seem to be
(n=1, B_4): x^2-2
(n=2, B_8): x^8-4*x^6+8*x^2-2
(n=3, B_12): x^12-8*x^10-34*x^4+18*x^8+23*x^2-2
(n=3, B_16): x^16-12*x^14+x^8+52*x^12+163*x^6-162*x^4-88*x^10+46*x^2-2

Setting x=1 in B_4, B_8, B_12, B_16 etc I get the very trivial 3-periodic
-1,3,-2,-1,3,-2,-1,3,-2,-1,3,-2,-1,3,-2,-1,..
which is quite different from A162180 (i.e., up to signs
essentially the same as A138034, A119910, A130784 and A131756).
So how do we correct A162180, or, alternatively, where is my calculation wrong?
Shouldn't B_4 be just x^4-2, so the B4 are nothing but
a quadrisection, taking each 4th polynomial of A135929, such that A162180
is just a quadrisection of A138034? (That's my favorite explanation...)
(Followup question: why is A162180 "triangle read by rows?")

I've read the Oydum, Hossein and Luzon references given in the OEIS,
and couldn't find any definition of the B4's ("buzz"), so
I cannot verify whether the author of A162180 got the correct definition.
He's using B_4=x^2-2 twice, in the comment and in the formula.
Is this a double error?

Richard

# Maple: Boub 4 defined by recurrence, as in the OEIS
B4 := proc(n)
        if n = 1 then
                x^2-2 ;
        elif n = 2 then
                x^8-4*x^6+8*x^2-2 ;
        else
                (x^4-4*x^2+2)*procname(n-1)-procname(n-2) ;
                expand(%) ;
        end if ;
end:
# Boub 4 printed
for n from 1 to 4 do
        b := B4(n) ;
        print(b) ;
od:

# Boub 4 at x=1 printed
for n from 1 to 16 do
        b := B4(n) ;
        printf("%d,",subs(x=1,b)) ;
od: