[seqfan] Re: OEIS Wiki: Offsets

[Joerg Arndt]

* Benoît Jubin <benoit.jubin at gmail.com> [Apr 14. 2015 19:47]:
> >> "Think long and hard whether a(0) is naturally defined. If yes, add it."
> 
> Among the first nine OEIS sequences, A000001(0)=0 and A000003(0)=0 should
> therefore be added.
> 
> >> Back to the original subject, I think it is worth while mentioning the
> example of sets & lists, and also insist on the example of general
> functions defined from some given value on (which may be more often 0 than
> 1, but also something else).
> 
> I like to think that there are two big purveyors of integer sequences:
> combinatorics and number theory. Sequences coming from combinatorics are
> often defined for all natural numbers (for instance, the number of group
> structures up to isomorphism on a set of size n) whereas sequences coming
> from number theory are often defined (or at least, interesting) for nonzero
> arguments, mainly because 0 is absorbing.
> 
> Benoit
> 

Another approach/guideline to "1 or 0?" is "multiplicative or additive by nature?".
Indeed we do have "multiplicative by nature" sequences with a term a(0)
that should not be there IMHO.

My own rule "give a(0) whenever you can" (which I did not mean to go
into the Wiki page) comes from the unfortunate omission of a(0) or
column-0 in many sequences about combinatorial objects.

Another telltale sign for a(0)=1 appears as
G.f.: (some natural expression) - 1.

Now if anybody challenges me to define "natural"/"by nature" I'll send
black helicopters in your general direction.

Best regards,  jj

> 
> [...]