[seqfan] name for class of sequences

[Bob Selcoe]

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