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Convoluted Convolved Fibonacci Numbers
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Pieter Moree

Max-Planck-Institut für Mathematik

Vivatsgasse 7

D-53111 Bonn

Germany

**Abstract:**
The convolved Fibonacci numbers are defined
by
. In this
note we consider some
related numbers that can be expressed in terms
of convolved Fibonacci numbers. These numbers appear in the numerical
evaluation of a constant arising in the study of the average density of
elements in a finite field having order congruent to (mod ).
We derive a formula expressing these
numbers in terms of ordinary Fibonacci and Lucas numbers. The
non-negativity of these numbers can
be inferred from
Witt's dimension formula for free Lie algebras.

This note is a case study of the transform
(with any formal series), which
was introduced
and studied in a companion paper by Moree.

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(Concerned with sequences
A000096
A006504
A001628
A001870
A001629
.)

Received November 12 2003;
revised version received April 20 2004.
Published in *Journal of Integer Sequences*, April 26 2004.

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