Collection of Python scripts, dedicated to symbolic computation of sums of powers of Fibonacci numbers:

Sum( fib(i)^p for i in [0 .. n] )

http://dmishin.blogspot.ru/2013/07/sums-of-powers-of-fibonacci-numbers.html

Derives formula for sums of Fibonacci powers. Formula is written in Python notation. Run without arguments to see usage details.

Example: Derivation of formula for p=1:

$python fibsums_general.py 1
Sum F(i)^1 =
= F(n) + F(n + 1) - 1 =
= F(n) + F(n + 1) - 1

With some simplification by hand, it gives well-known formula: Sum F(i) = F(n+2)-1.

Converts formula, containing F(i)**n into LaTeX notation. Formula is read from stdin, empty line terminates.

Set of tests of formulas, derived by author. Edit code to add new tests.

Simplifies expression of form:

AF(x+N) + BF(x+N-1)

where A, B, N are integers. Run script and enter A B N, separated by spaces.

Python3 and Sympy are required.

Not intended for installation.