[seqfan] Re: Partitions and Dice

Richard Mathar mathar at strw.leidenuniv.nl
Sat Feb 21 16:09:48 CET 2009

ftaw> From seqfan-bounces at list.seqfan.eu Sat Feb 21 01:32:00 2009
ftaw> To: seqfan at seqfan.eu
ftaw> Date: Fri, 20 Feb 2009 19:06:13 -0500
ftaw> From: franktaw at netscape.net
ftaw> Cc: toby at gottfriedville.net
ftaw> Subject: [seqfan]  Partitions and Dice
ftaw> I was just looking at A102420 and A102422:
ftaw> http://www.research.att.com/~njas/sequences/?q=id%3AA102420|id%3AA102422
ftaw> Mostly, I was wondering if this is the way we should generally handle 
ftaw> sequences which are naturally zero after some point.  Or would it be 
ftaw> better to truncate them and apply the "fini" and "full" keywords?  
ftaw> (A000004 and A000007 would be exceptions, of course.)

If the definition generates values of 0 (like in the two cases mentioned),
placing zeros is a good idea, because this enhances contrast relative
to other sequences that may coincide at the non-zero places. That is, if we
look up a subsequence, the number of "false" hits can be reduced if zeros are
explicitly present.

There are other cases, where the definition generates only a finite number
of terms, and then the sequences are "fini" and "full" by definition.
In summary: Not using "fini" and "full" in A102420 or A102422 makes
sense, because there are indeed trailing zeros and not NaN's (=not-a-number
in Java/C/Fortran/FITS/IEEE speak), and because these terms (=zeros)
are known and valid counts.

Richard Mathar

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