Special formulas involving polygonal numbers and Horadam numbers

Abstract

Some convolution-type identities involving polygonal numbers and Horadam numbers are derived. The method of proof is to properly relate the generating functions to each other. Additionally, we prove a general non-convolutional result involving these number families and discuss some of the consequences.

Keywords

• horadam sequence
• polygonal numbers
• triangular numbers
• fibonacci sequence
• generating function
• recurrence relation