On (d, k) Sequences Not Containing a Given Word

A sequence of zeros and ones is called a (d,k)-sequence if it does not contain runs of zeros of length either less than d or greater than k, where d and k are arbitrary, but feed, positive integers and d < k. For a given pattern w, we enumerate exactly and asymptotically (d,k) sequences of length n that do not contain a given word w. We use techniques of analytic algorithms such as generating functions, combinatorial calculus, and complex asymptotics