Clark, One suggestion is for you (or someone else) to try gfun on the sequence, giving gfun 50 terms (or more). And telling it to look for a linear recurrence of order up to 8, say - and then steadily increasing the number of terms and the limit on the order, until it starts taking too long. If there IS a linear recurrence, then the theory says that gfun will find it, given enough terms and enough time. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Tue, Jan 2, 2018 at 10:47 AM, Kimberling, Clark <ck6@evansville.edu> wrote:
Here's a question about possible linear recurrence for A296220, which gives the solution of the complementary equation
a(n) = a(0)*b(n-1) + a(1)*b(n-2), where a(0) = 1, a(1) = 2, b(0) = 3,
and (a(n)) and (b(n)) are increasing complementary sequences. In the Formula section, it is conjectured that
a(n) = a(n-1) + a(n-7) - a(n-8) for n > 20.
However, that sequence (using the same a(0),...a(20) as A296220) includes 244, but A296220 doesn't. So, the question is, does A296220 satisfy some other recurrence?
Best wishes for the new year!
Clark Kimberling
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