[seqfan] Re: name for class of sequences

[israel at math.ubc.ca]

... a monic polynomial with all non-leading coefficients nonpositive 
integers.

Cheers,
Robert Israel

On Jan 21 2015, Frank Adams-Watters wrote:

>I don't know about a name, but these are precisely the sequences whose 
>generating function is the reciprocal of a monic polynomial.
>
>Franklin T. Adams-Watters
>
>-----Original Message-----
>From: Bob Selcoe <rselcoe at entouchonline.net>
>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>Sent: Wed, Jan 21, 2015 3:28 pm
>Subject: [seqfan] name for class of sequences
>
>
>Hello Seqfans,
>
>Consider a class of sequences generated by the recurrence:
>
>a(n) = q*a(n-f1) + r*a(n-f2) + s*a(n-f3)... + y*a(n-fz)
>
>where:
>
>i.  the only seed value is a(0) = 1, and a(n) n < 0 = 0;
>ii.  f1..fz and q,r,s,..y are positive integers, and
>iii.   f1 < f2 .. < fz
>
>Among the most basic sequences in this class are:
>
>A000045  Fibonacci:  a(n) = a(n-1) + a(n-2);
>A000931  Padovan:  a(n) = a(n-2) + a(n-3); and
>A000129  Pell numbers:  a(n) = 2*a(n-1) + a(n-2)
>
>The class could be called "ordered partition sequences" or "composition
>sequences" because for all such sequences, a(n) is the number of
>compositions (ordered partitions) of n into q sorts of  f1's, r sorts 
>of
>f2's, s sorts of f3's... y sorts of fz's.
>
>This may be very basic, but does a name for such a class already exist?
>
>Thanks,
>Bob Selcoe
>
>
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