accident?

[r.shepherd]

From: "Emeric Deutsch" <deutsch at duke.poly.edu>
To: <seqfan at ext.jussieu.fr>
Cc: "N. J. A. Sloane" <njas at research.att.com>
Sent: Saturday, June 14, 2003 3:51 PM
Subject: Re: accident?


> Dear seqfans,
> Let me reformulate my puzzling remark. Hopefully
> in a clearer way.
> I type in
> 1,2,5,12,29,70.
> I get 3 sequences; I list the three terms following the above ones:
> A000129: 169 408 985
> A054196: 169 410 1005
> A054198: 169 409 995
> The 7th terms coincide, the 8th terms are very close, and even
> the 9th terms are close enough.
> It happens very often.
> Thanks for your comments.
> Emeric

Well, I can only offer speculation, some of which may inspire criticism
and get you a "real" (i.e., more statistical/numerically analytic) answer.

Perhaps (and some of these may be overlapping speculative reasons):
1) there is "natural selection" that determines which sequences actually
go into the OEIS (perhaps sequences deemed more useful)
2) there are arbitrary constraints ("artificial selection") such as sequence
shouldn't relate to some arbitrary large number (e.g., 2003)
3) we are not as creative as we could be so we are thinking only
slightly different thoughts
4) the concepts human beings study are highly related because of the
types of research work that is supported and encouraged by funding
5) sequences that are different require time (i.e., extra terms) to
"express their individuality" just as older individuals have more time
to develop unique characteristics than younger individuals
6) very many sequences are submitted by a few individuals who are
interested in a particular area of study (e.g., lattices, counting trees,
counting graphs, etc., and (similar to (5) many of these objects with
differentiating characteristics cannot be different until larger terms
where the constraints have a visible effect  (I've probably seen this
with some actual-chess-rule-related sequences where the board becomes
crowded as more and more pieces appear on it but the board doesn't
grow correspondingly.).
7) "great minds think alike" :^) (sort of)
8) yes, accident
9) some might even ponder that a Watchmaker has a Design for
certain patterns to unfold in certain ways at certain times for
certain (unknown to us at the time) reasons.

(I wouldn't be counting "penny graphs" right now if I hadn't
accidentally hit on 1,1,2,4,9(with error),20+ leading to
1,1,2,4,10,25,....  (*lots* of sequences having 1,1,2,4,(9 or 10)
at the beginning of them) Guess what?  Penny graphs and other
closely related graphs tend to have application in wireless
telephone transmission tower positioning.  Although I never
sought it ought, I did spend about 10 years working in
telecommunications very recently....  Although I'm not
really interested in telecommunications per se, I find this
particular combinatorics problem of counting graphs interesting
at this time -- but then I'm unemployed and need to do something
while decisions are ponderously made by powers-that-be.)

After all there can be an infinite number of sequences which differ only
in, say, three terms (and a small fraction of that  number *could* already
be in the OEIS database.  If it's somehow bothersome (depending upon
your own analysis), we could "reverse-engineer" some sequences so that
those, say, 7th, 8th, and 9th terms vary greatly.

Interesting (philosophical but not necessarily mystical) puzzle, though,
Rick