  A dispersed Dyck path (DDP) of length n is a lattice path on $N\times N$ from
(0,0) to (n,0) in which the following steps are allowed: "up" (x, y) $\to$
(x+1, y+1); "down" (x, y) $\to$ (x+1, y-1); and "right" (x,0) $\to$ (x+1,0). An
ascent in a DDP is an inclusion-wise maximal sequence of consecutive up steps.
A 1-ascent is an ascent consisting of exactly 1 up step. We give a closed
formula for the total number of 1-ascents in all dispersed Dyck paths of length
n, A191386 in Sloane's OEIS. Previously, only implicit generating function
relations and asymptotics were known.
