You might take a look at the book by A Gill, Linear Sequential Circuits, McGraw Hill, 1965. The subject called Systems Theory, very popular in the 1960s, studies problems like those There are many books (Zadeh & Desoer is a classic) The titles usually say Linear Systems Theory, but that covers a lot of ground. 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 Thu, Jan 14, 2021 at 12:45 AM Hilarie Orman <ho@alum.mit.edu> wrote:
I am interested in some general ways of defining sequences s[i].
1. s[n+1] = f(s[n])*s[n-1] + f(s[n-1])*s[n] If f is the constant function "1", then this is the Fibonacci sequence.
2. s[n+1] = g(s[n]){s[n], s[n-1], ..., s[0]} Here, g is a function that has a number as an input and produces a multivariate function that is applied to previous sequence values. g could be, for example, a linear function with k terms using coefficients derived from s[n].
3. s[n+1] = g(s[n]){t[n], t[n-1], ... t[0]} where t is a sequence defined on i=0...inf. As before, g is a multivariate function derived from the number s[n].
Is there some standard terminology for these methods that I could use to find prior work? The keywords just cause Google to latch onto well-known recursive sequences.
Thanks,
Hilarie
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