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In how many ways can one tile the rectangle?

Source: Austrian Mathematical Olympiad 2003, Part 2, D2, P2

June 18, 2011
geometryrectanglecombinatorics unsolvedcombinatorics

Problem Statement

We are given sufficiently many stones of the forms of a rectangle 2×12\times 1 and square 1×11\times 1. Let n>3n > 3 be a natural number. In how many ways can one tile a rectangle 3×n3 \times n using these stones, so that no two 2×12 \times 1 rectangles have a common point, and each of them has the longer side parallel to the shorter side of the big rectangle?
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