This is a spot of Pari/GP code to guess a linear recurrence from a vector of numbers. If successful the result is pretty printed. For example,

recurrence_guess([1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609]); => Recurrence length=3 Coefficients v[n-3]* [4, -8, 5] *v[n-1] = v[n] v[n] = v[n-1]* [5, -8, 4] *v[n-3] Characteristic polynomial x^3 - 5*x^2 + 8*x - 4 = factors (x - 2)^2 root 2.00000 x - 1 root 1.00000 Generating function (1 - 2*x + 2*x^2)/(1 - 5*x + 8*x^2 - 4*x^3) = partial fractions 1/(1 - x) - 1/(1 - 2*x) + 1/(1 - 2*x)^2 As powers n * 2^n + 1

The guess is found by a simple `matsolve()`

. Linear recurrences
include powers, polynomials, and polynomials times powers. Similar code can
be found in
`findrec()`

by Charles R. Greathouse and
`ggf()`

in the OEIS
Sequence Tools. Nice display here in various forms is the tedious part.
Of course "nice" is a matter of personal preference and the output is still
quite mechanical.

`recurrence-guess.gp`

is
free software (free
as in freedom), published under the terms of the
GNU General Public
License (v3 or higher). Download version
6 here. Requires my
`pol-pfrac.gp`

.

`recurrence-guess.gp`

(38k, and sig)

`recurrence-guess-6.tar.gz`

(37k, and sig)

Just `recurrence-guess.gp`

(and
`pol-pfrac.gp`

) is
enough to run. The `tar`

file includes some self-tests. The sig
files are Gnu PG ascii armoured signatures
generated from my key.

This page Copyright 2016 Kevin Ryde, except for the GPLv3 logo which is Copyright Free Software Foundation and used here in accordance with its terms.