Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence

The study of recurring numerical sequences usually involves a restricted context of circulation and communication of new ideas and abstract mathematical properties. On the other hand, authors of the history of mathematics books tend to emphasize, in an almost restrictive way, anecdotal curiosities about the Fibonacci sequence. Given this context, in this work, we find a proposal for exploring arithmetic and combinatorial properties using the notion of board and tiles, which correspond to properties of the Padovan or Cordonier numerical sequence. Through some elements, we will demonstrate that such an approach involves potential for application in the classroom to provide a relevant role for visualization and learning.