论文信息 - Convoluted convolved Fibonacci numbers

Convoluted convolved Fibonacci numbers

The convolved Fibonacci numbers F (r) j are deflned by (1ixix 2 ) ir = P j‚0 F (r) j+1 x j . 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 flnite fleld having order congruent to a (mod d). 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 1 P djn „(d)f(z d ) n=d (with f any formal series), which was introduced and studied in a companion paper by Moree.

P. Moree

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