[seqfan] Re: Tribonacci confusion

[Arthur O'Dwyer]

FWIW, I agree with Robert's general direction:
(1) Every sequence that currently refers to "the tribonacci numbers"
without disambiguation, should refer to "the tribonacci sequence Axxxxxx"
for clarity.
(2) Perhaps A000073 should be "the tribonacci numbers," whereas the others
should be merely "the tribonacci sequence starting with..." or even "the
*generalized* tribonacci sequence starting with...", in the same way that
we talk about "generalized Fibonacci sequences."

I've submitted a couple of minor edits in that direction, disambiguating
and adding cross-refs, but I stopped short of adding the word
"generalized". I'd support someone more authoritative than me going ahead
with it, though. :)
https://oeis.org/draft/A113153
https://oeis.org/draft/A231575

–Arthur


On Wed, Jul 24, 2024 at 10:22 AM Neil Sloane <njasloane at gmail.com> wrote:

> Robert,  I am well aware of that ambiguity, but life is full of
> ambiguities, and I don't regard that one as especially important.  Or
> worrying.  Yes, A73 is clearly the most important variant.
>
> We could certainly add a comment to all of them saying the following:
>
> The name "tribonacci number" is less well-defined than "Fibonacci number".
> A000073 (which begins 0, 0, 1) is probably the most important version, but
> the name has also been applied to A000213, A001590, and A081172.
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Wed, Jul 24, 2024 at 10:05 AM <israel at math.ubc.ca> wrote:
>
> > A000073, A000213, A001590 and A081172 all claim to be "Tribonacci
> numbers"
> > according to their Names. All are solutions of the recurrence a(n) =
> > a(n-1)
> > + a(n-2) + a(n-3), but the initial conditions are different: a(0)=a(1)=0,
> > a(2)=1 for A000073, a(0)=a(1)=a(2)=1 for A000213, a(0)=0, a(1)=1, a(2)=0
> > for A0001590, a(0)=1, a(1)=1, a(2)=0 for A081172. Moreover, the Names of
> a
> > number of other sequences such as A113153 and A092836 refer to "the
> > tribonacci numbers" without specifying which version is meant.
> >
> > Can we (or should we) reduce the confusion? I think A000073 is the most
> > popular choice for "the tribonacci numbers". We could perhaps adopt the
> > convention that this is the preferred choice, and change the Names of the
> > other contenders, perhaps with Comments such as "Sometimes called the
> > tribonacci numbers, but ...".
> >
> > At the very least, all the contenders should have Comments referring to
> > their rivals, and the other sequences should refer to "the tribonacci
> > numbers (Axxxxxx)".
> >
> > What do you think?
> >
> > Cheers,
> > Robert
> >
> > --
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> >
>
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