Title: Recurrence Relations of Linear Tilings

Abstract: Let U ⊆ ℕ and let T be a linear tiling of a 1 x n board using 1 x i polyomino tiles where u is in U. We define T_U(n) to be the set of linear tilings of length n using tile sizes in U. Classically, when U = { 1, 2} these tilings are known as the Lucanomial tilings and they follow the Lucas sequence. Now, let U and V be distinct subsets of the natural numbers. In this talk, we will provide some general results and supportive examples of a large family of linear recurrence relations between the sequences T_U(n) and T_V(n) for fixed sets U and V. This is joint work with Christopher O'Neill and Pamela E. Harris.