Combinatorial Identities for Incomplete Tribonacci Polynomials

Authors

Mark Shattuck, University of Tennessee

Abstract

The incomplete tribonacci polynomials, denoted by T_n^(s)(x), generalize the usual tribonacci polynomials T_n (x) and have been shown to satisfy several algebraic identities. In this paper, we provide a combinatorial interpretation for T_n^(s)(x) in terms of weighted linear tilings involving three types of tiles. This allows one not only to supply combinatorial proofs of earlier identities for T_n^(s)(x) but also to derive new ones. In the final section, we provide a formula for the ordinary generating function of the sequence T_n^(s)(x) for a fixed s, as previously requested. Our derivation is combinatorial in nature and makes use of an identity relating T_n^(s)(x) to T_n (x).

Recommended Citation

Shattuck, Mark (2015). Combinatorial Identities for Incomplete Tribonacci Polynomials, Applications and Applied Mathematics: An International Journal (AAM), Vol. 10, Iss. 1, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol10/iss1/3