  Wu showed that certain sums of products of binomial coefficients modulo 2 are
given by the run length transforms of several famous linear recurrence
sequences, such as the positive integers, the Fibonacci numbers, the extended
Lucas numbers, and Narayana's cows sequence. In this paper we show that the run
length transform of such sequences are 2-regular sequences. This allows us to
obtain Wu's results and some new ones using the computer program Walnut,
eliminating the need for long technical proofs.
