Convoluted convolved Fibonacci numbers

Abstract

The convolved Fibonacci numbers F_j^(r) are defined by (1-z-z^2)^{-r}=\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers that can be expressed in terms of convolved Fibonacci numbers are considered. These numbers appear in the numerical evaluation of a certain number theoretical constant. This note is a case study of the transform {1/n}\sum_{d|n}mu(d)f(z^d)^{n/d}, with f any formal series and mu the Moebius function), which is studied in a companion paper entitled `The formal series Witt transform'.

12 pages, 3 tables

References in corpus (1)

• On the average number of elements in a finite field with order or index in a prescribed residue class

Cited by in corpus (6)

• On the distribution of the order and index of g(mod p) over residue classes II
• The formal series Witt transform
• On the distribution of the order and index of g(mod p) over residue classes III
• On the distribution of the order over residue classes
• Convolved Fibonacci Numbers and their applications
• Multi-colored dimer models in one-dimension: lattice paths and generalized Rogers--Ramanujan identities