Twice the total area of all nonnegative lattice paths from (0,0) to (n,0) where the allowed steps at (x,y) are (h,v) with h in {1..max(1,y)} and v in {-1,0,1}.

A337863

Twice the total area of all nonnegative lattice paths from (0,0) to (n,0) where the allowed steps at (x,y) are (h,v) with h in {1..max(1,y)} and v in {-1,0,1}.