[seqfan] Some Recurrence Sequences
Harvey P. Dale
hpd1 at nyu.edu
Tue Apr 26 14:35:32 CEST 2011
Consider recurrence sequences with this pattern: a(0)=x, a(1)=y,
a(n)=x *a(n-1) + y*a(n-2). The OEIS currently contains at least seven
such, corresponding to these respective values of x and y: (1,1), (1,2),
(1,3), (1,4), (2,2), (2,3), and (2,4). Limiting the values of x and y
to numbers greater than zero but less than six, there are 18 other
sequences that are not now in the OEIS: (1,5), (2,1), (2,5), (3,1),
(3,2), (3,3), (3,4), (3,5), (4,1), (4,2), (4,3), (4,4), (4,5), (5,1),
(5,2), (5,3), (5,4), and (5,5). Are these of sufficient interest to
submit them to the OEIS? If so, I'll try to do that over the next few
days, but I'd appreciate being reminded about how to get a block of A
numbers reserved so that each one submitted would be contiguous to the
others.
Best,
Harvey
P.S. If anyone wishes to generate these sequences, here's an efficient
way to do so: f[x_,y_]:=LinearRecurrence[{x,y},{x,y},20].
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