Partitioning the Natural Numbers with Fibonacci-like Sequences

Levi Montee
Graduate Student
University of Wisconsin-Milwaukee

Famously seen in the displacement of seeds in a sunflower, the branching of tree limbs or enumerating results in a variety of combinatorics problems, the Fibonacci sequence has become one of the most recognizable sequences in mathematics. Beginning f0 = 0, f1 = 1, and continuing fn+1 = fn + fn-1, this simple recurrence relation has been well studied for centuries. In this talk, we will investigate sequences determined by the same recurrence relation given alternative starting points. We attempt to classify these sequences, see which familiar Fibonacci properties are kept intact, and examine when two such sequences share terms. Ultimately, we aim to find a set of disjoint Fibonacci-like sequences that partition the natural numbers, and see how these might be useful in solving particular logic games/puzzles.