Generating Function for the Figurative Numbers of Regular Polyhedron

Abstract

In this paper, we are going to demonstrate a method for determining the generating functions of tetrahedral, hexahedral, octahedral, dodecahedral, and icosahedral figurative numbers. The method is based on the differences between the members of the series of the mentioned figurative numbers, as well as on the previously specified generating functions for the sequence ∑n≥0n+1xn and geometric sequence ∑n≥0xn.