On a question of Cooper and Kennedy

Cooper and Kennedy asked whether arbitrary powers of elements which are a solution of a linear recurrence with constant coefficients (for instance:Fibonacci numbers) also fulfill such a recurrence. The answer is yes; "Hadamard product".
I gave also pointers to the very useful programs gfun and zeil, by Salvy and Zimmermann and Zeilberger, respectively.
When I will have time, I will provide links here to the respective software servers.


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