  Seth (Mathematics Stack Exchange, http://math.stackexchange.com/q/1812699)
posed a problem that is equivalent to the following: how many binary strings of
length n have exactly k pairs of consecutive 0s and exactly m pairs of
consecutive 1s, where the first and last bits are considered as being
consecutive? In this paper, we provide a closed form solution which also solves
a related problem with some interesting connections to other combinatorial
sequences.
