Through the tiling glass: Tribonacci identities

Using combinatorial tiling arguments, we explore identities involving the Tribonacci and Tribonacci-Lucas numbers and related sequences, including the Fibonacci numbers, Narayana’s cows sequence, and the Padovan numbers. The tiling framework yields results that both unify and extend existing work. In particular, we derive new identities and provide new combinatorial proofs of several known ones.