|Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2|
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.
(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.