MathDB

A merida path of order

2n

is a lattice path in the first quadrant of

xy

- plane joining

(0,0)

(2n,0)

using three kinds of steps

U=(1,1)

D= (1,-1)

and

L= (2,0)

, i.e.

U

joins

x,y)

(x+1,y+1)

etc... An ascent in a merida path is a maximal string of consecutive steps of the form

U

. If

S(n,k)

denotes the number of merdia paths of order

2n

with exactly

k

ascents, compute

S(n,1)

and

S(n,n-1)

Problem Statement