Resumen de Tilings of (2 × 2 × n)-board with coloured cubes and bricks

Laszlo T. Nemeth

• Several articles deal with tilings with squares and dominoes on 2- dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with coloured cubes and bricks on a (2 × 2 × n)-board in three dimensions. After a short introduction and the definition of breakability we show a way to get the number of the tilings of an n-long board considering the (n − 1)-long board. It describes recursively the number of possible breakable and unbreakable tilings. Finally, we give some identities for the recursions using breakability.