An Explicit Formula for Supergeneralized Leonardo p-numbers

In this paper, we introduce the supergeneralized Leonardo $p$

-numbers, $\mathcal{L}_{p,k,\mathbf{x}}(n)$ , which extend the definition of the generalized Leonardo $p$

-numbers, introduced by Kuhapatanakul and Ruankong, by not requiring $\mathcal{L}_{p,k}(0) = \cdots = \mathcal{L}_{p,k}(p) = 1$ but allowing the first $p+1$

initial values to be chosen freely. We then investigate the structure of these sequences, show that they are related to the Fibonacci $p$

-numbers, and provide an explicit formula for $\mathcal{L}_{p,k,\mathbf{x}}(n)$ when $n > p$

An Explicit Formula for Supergeneralized Leonardo p-numbers

Clemens Schütz and Kristian Kelly Department of Mathematics University of Vienna Vienna Austria

Clemens Schütz and Kristian Kelly
Department of Mathematics
University of Vienna
Vienna
Austria