Growth rates of rabbit populations in 2D

(M.Sc. Lothar Dirks)

In the 1202 book Liber Abaci, Leonardo da Pisa (Fibonacci) uses what was later named the Fibonacci sequence to describe the growth of a fictional population of rabbits. A similar scenario is formed by the question of the number of sequences over the two-letter alphabet {0,1} with length n in which no two consecutive entries are 1. Not surprisingly, this number corresponds to the (n+2)-th Fibonacci number. For the two-dimensional analogue, on the other hand, where the question is the number of matrices without adjacent ones, no explicit formula is known to date.
The aim of the project is to determine explicit formulas for certain matrix sizes via pattern recognition as done in the one-dimensional case (see figure).

Basic knowledge in the fields of calculus and linear algebra is recommended. The duration of the work within the research group should be at least four weeks. The project includes a written paper and a presentation in a seminar.