Algorithm for Calculating the Exact Amount of n-bit Sequences with at Least One Run of Length k (k ≤ n)

A run of length k in a sequence of n bits (0, 1) is an equal bits string preceded or succeeded by a different bit (or none). In this paper a computational algorithm for calculating the exact amount of binary sequences of length n, containing at least one run of length k (k ≤ n) is presented. The immediate application of this algorithm is to calculate the exact probability distribution of the number of n-bit sequences with containing at least one run of length k, and no one greater than k, for use for example as part of a test for randomness