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## Definitions

• The -Fibonacci- sequence (the th term of which is denoted ) is defined recursively by the following statements:
• If , then .
• .
• , .
Note that this idea encompasses both the -Fibonacci sequence and the Fibonacci- sequence.
• means that has the following properties:
• .
• For all such that , it follows that .
• is the least positive integer satisfying these properties.
• means that has the following properties:
• • For all such that , it follows that .
• .
• is the least positive integer satisfying these properties.
Note: is then the function that gives the period of the -Fibonacci- sequence in modulo .
• means that has the following properties:
• is the number of that satisfy the property that all from to , inclusive, satisfy the property that , where goes from to , inclusive.
• means that has the following properties:
• is the number of that satisfy the property that all from to , inclusive, satisfy the property that , where goes from to , inclusive.    Next: Theorems Up: k-Fibonacci-q numbers and new Previous: k-Fibonacci-q numbers and new   Contents
Gregory Stoll 2000-04-08