Asymptotic number of isometric generalized Fibonacci cubes

For a binary word f, let Q(d)(f) be the subgraph of the d-dimensional cube Qd induced on the set of all words that do not contain f as a factor. Let g(n) be the set of words f of length n that are good in the sense that Q(d)(f) is isometric in Q(d) for all d. It is proved that lim(n-->infinity) vertical bar g(n)vertical bar/2(n) exists. Estimates show that the limit is close to 0.08, that is, about eight percent of all words are good. (C) 2011 Elsevier Ltd. All rights reserved.