The number of n-bit words with a given longest run of 1's is computed. A relation between these numbers and the Fibonacci numbers is outlined and investigated.

runs in binary words, Fibonacci numbers, generating function

R. Rom, "Distribution of Runs in Binary Words," in IEEE Transactions on Computers, vol. 27, no. , pp. 1087-1089, 1978.
doi:10.1109/TC.1978.1675003