Recursive sequences

[Tanya Khovanova]

seems to equal A114951.
subscribe anymore to the Monthly, and I have lost the photocopy of the 
solution.)
 
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Tanya Khovanova wrote:

> Right now I have the following types of sequences there:
>     * a(n) = d * a(n-1) - a(n-2).
>     * a(n) = d * a(n-1) + d * a(n-2).
>     * a(n) = a(n-1) + a(n-2).
>     * a(n) = d * a(n-1) + a(n-2).
>     * a(n) = d * a(n-1). Geometric progressions.
>     * a(n) = a(n-1) + d. Arithmetic progressions.
>     * a(n) = a(n-1). Constants.
> 

Nice work! Do you consider more general second order recurrences:
a(n) = c_1 * a(n-1) + c_2 * a(n-2)
and the inhomogenous case:
a(n) = c_1 * a(n-1) + c_2 * a(n-2) + b(n)?

In SAGE there a generator function for this type of recurrences.
See the source code in sage/combinat/sloane_functions:
http://modular.math.washington.edu/sage/ Browse code:
http://sage.math.washington.edu/sage/hg/sage-main/file/5ed4f056fa9e/sage/combinat/sloane_functions.py

Feel free to contribute!

Jaap