[seqfan] Re: Tribonacci confusion

[Neil Sloane]

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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