On the Number of Balanced Words of Given Length and Height over a two-Letters alphabet
Résumé
We exhibit a recurrence on the number of discrete line segments joining two integer points using an encoding of such segments as balanced words of given length and height over the two-letter alphabet {0,1}. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes and provide generating functions in this case. We end by studying the asymptotical behaviour of the previous recurrences.