Counting Palindromic Binary Strings Without r-Runs of Ones
Michael A. Nyblom · RMIT Research Repository (RMIT University Library) · 2013
A closed-form expression is derived for the enumeration of all palindromic binary strings of length n> r having no r-runs of 1’s, in terms of the r-Fibonacci sequence. A similar closed-form expression for the number of zeros contained in all such palindromic binary strings is derived in terms of the number of zeros contained in all binary strings having no r-runs of 1’s. 1