Tiling a Strip with Triangles

Abstract

In this paper, we examine the tilings of a $2\times n$ "triangular strip" with triangles. These tilings have connections with Fibonacci numbers, Pell numbers, and other known sequences. We derive several different recurrences, establish some properties of these numbers, and give a refined count for these tilings (i.e., by the number and type of triangles used) and establish several properties of these refined counts.