[seqfan] Re: Offsets for Recurrence Sequences
Creighton Kenneth Dement
creighton.k.dement at mail.uni-oldenburg.de
Thu Apr 23 17:52:31 CEST 2009
[snip]
> There is no need for this; the reader would not become confused if the
> proper notation, including correctly type-set indices, were chosen.
I may be the only one, but I think it would be nice to see an example of
what is meant by "the" proper notation in the case of setting up relations
between sequences with different offsets.
> ckd> Why are there two essentially the same (core) Lucas sequences with
> offsets
> ckd> 0 (A000032) and 1 (A000204) but apparently no corresponding Fibonacci
> ckd> sequence with an offset of 1? For example, A000032 has a comment
> "Starting
> ckd> (1, 3, 4, 7, 11,...) = row sums of triangle A131774." with no mention
> of
> ckd> this for A000204. IMHO, it seems needlessly confusing.
>
> This is confusing because the comment is of poor quality. Of course, the
> comment should say "row sums of row n are A000032(n)", aligning the
> (correct) notation of the row-index in the table/triangle
> with the (correct) index in the linear sequence.
My main point is that if A000045 with its nearly limitless combinatorial
interpretations (many of which may actually be twice the sequence or not
include a certain value), is not "good enough" to earn a second version of
itself with a different offset, then it is confusing why any other
sequence would be given a greater VIP status. I think if someone's
combinatorial interpretation of a set of objects produces a sequence found
in the OEIS and this does not include its initial value or has to be left
undefined, it should be left as a comment. I hope I'm not alone in
wholeheartedly agreeing with Peter's post... also, very much like the "*"
notation to denote an undefined term.
[snip]
> ckd> A quick glance reveals A098301 + A011916 = A123480 and what should be
> a
> ckd> simple case of sending in a comment becomes more difficult because
> the
> ckd> offsets are different. Would it be o.k. just to write A098301 +
> A011916 =
> ckd> A123480, offsets differ?
>
> This just reveals some laziness.
I don't agree this is a matter of laziness. Admittedly, there is sometimes
a fine line between trying to do something as efficiently as possible and
trying to do something so that in the end there will be more free time to
do other things.
Thanks again for the replies!
Sincerely,
Creighton
The notation without indices should be
> left
> to constants (which one can add,multiply, subtract etc) and perhaps to
> union, intersection etc of sequences, but the explicit words like UNION,
> SET-MINUS, INTERSECT or \ are clearer if sequences are mixed/complemented
> etc.
> Note that indices, in the mathematical context and in any programming
> languages, DO matter. Leaving this information out does not make sense and
> just pushes the burden to get them right to the OEIS user (or editors).
> It is needed by any reader who has to deal with the sequences, anyway.
>
> RJM
>
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