K+1 Parametric Sequences And Taxicab-Type Numbers

Abstract

In this work, the idea of the taxicab number is generalized to taxicab-type numbers with respect to: bases and  generating sets, by defining a special type of sequences named k+1 parametric sequencses over a given subset of the set of natural numbers. The taxicab-type numbers with respect to the basis are related with the classical taxicab numbers. Both of the taxicab-type numbers over different domains are generated using Mathematica and are listed.