Problem Statement

Leonardo numbers   are also known as the   Leonardo series.

The   Leonardo numbers   are a sequence of numbers defined by:

This task will be using the 3rd equation (above) to calculate the Leonardo numbers.

Edsger W. Dijkstra   used   Leonardo numbers   as an integral part of his   smoothsort   algorithm.

The first few Leonardo numbers are:

(The last task requirement will produce the Fibonacci numbers.)

Show all output here on this page.

Let's start with the solution:

#!/bin/bash

function leonardo_number () {
    L0_value=${2:-1}
    L1_value=${3:-1}
    Add=${4:-1}
    leonardo_numbers=($L0_value $L1_value)
    for (( i = 2; i < $1; ++i))
    do
       leonardo_numbers+=( $((leonardo_numbers[i-1] + leonardo_numbers[i-2] + Add)) )
    done
    echo "${leonardo_numbers[*]}"
}