MathDB

We call a sequence of integers a Fibonacci-type sequence if it is infinite in both ways and

a_{n}=a_{n-1}+a_{n-2}

for any

n\in\mathbb{Z}

. How many Fibonacci-type sequences can we find, with the property that in these sequences there are two consecutive terms, strictly positive, and less or equal than

N

? (two sequences are considered to be the same if they differ only by shifting of indices)
Proposed by I. Pevzner

Problem Statement