Tiling a Strip with Triangles

  • John Bodeen
  • Steve Butler
  • Taekyoung Kim
  • Xiyuan Sun
  • Shenzhi Wang
Keywords: Triangle tilings, Fibonacci numbers, Pell numbers


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.

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