[seqfan] Re: Duplicates

Joseph S. Myers jsm at polyomino.org.uk
Sun Sep 13 18:42:04 CEST 2009

On Sun, 13 Sep 2009, Ignacio Larrosa Cañestro wrote:

> Sequences
> http://www.research.att.com/~njas/sequences/A001835
> (a(n) = 4a(n-1) - a(n-2); a(0) = a(1) = 1)
> and
> http://www.research.att.com/~njas/sequences/A079935
> are the same, except for a initial extrra 1.

There are actually lots of sets of sequences that are the same apart from 
the initial terms, and have cross references from one to another to point 
out this similarity (these two already have the cross references).

I don't think adding more such almost-duplicates is really encouraged - 
you're meant to omit the initial terms when searching to see if a sequence 
is already there, and can always add a comment to an existing sequence 
about the significance of a variant with different initial terms - but at 
the same time, having existing such variants present does help people who 
search without omitting (enough) initial terms.  And there are cases where 
sequences agree except for initial terms but you don't really want to 
consider them almost-duplicates (it would seem odd to consider all 
sequences with only finitely many nonzero terms to be almost-duplicates of 
A000004, for example).

See my previous comments about how it should be possible for OEIS to know 
how such sets of sequences are related so that extending or adding a 
b-file to one or extending a b-file has the effect of extending or adding 
or extending a b-file for all the sequences in such a set.  (This doesn't 
need to be done by the core OEIS software; after the move to a wiki, an 
externally maintained bot could propagate changes from one sequence to 
another related sequence.)  You could extend this idea by defining one 
sequence in such a set to be the main sequence that gets all the comments 
etc., and making the others just have the variant set of terms (so they 
can be found by searches, used in transformations along with other 
sequences, etc.) and a pointer to the main sequence.

Here are a few such almost-duplicate sets (from linear recurrences, like 
the one you give) I've noticed before:


I do not believe there are any *exact* duplicates (same initial terms and 
offset) in these sets; they are just sequences whose only differences are 
offsets and initial terms.  There are already various cross-references 
between the sequences in these sets pointing out the similarities.  So I 
don't think there's anything to change in OEIS at present regarding these 
sequences, but it might hopefully be possible in future to create 
better-defined links between such sets of sequences.

Joseph S. Myers
jsm at polyomino.org.uk

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