[seqfan] Tribonacci confusion

[israel at math.ubc.ca]

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