Catalan Numbers
                 =# ways to “parenthesize” (n+1) objects
       Matrix Power Term   Graph
(1((23)4))   A12A23A32A24A42A21
(((12)3)4)   A12A21A13A31A14A41
(1(2(34)))   A12A23A34A43A32A21
((12)(34))   A12A21A13A34A43A31
((1(23))4)   A12A23A32A21A14A41
= number of special paths on n departing from 1 once
v Pass 1, (load=advance, multiply=retreat), Return to 1