In this work we propose to enumerate certain particular paths defined in N*N by:
C(x,y)=C(x-2, y)+C(x-1, y-1)+C(x, y-2), x>2, y>2
C(1, y)=C(0, y-2)+C(1, y-2)
C(0, y)=1 y=0, 2, 4, ...
C(y, y)=C(y-2,y)+C(y-1, y-1)
C(y, y-2)=0
We thus establish an array of values from which we form sequences of well-known numbers, notably a sequence of numbers already encountered in [1] by G.Kreweras Where it is a question of counting uncrossed partitions of a cycle.
We also find a link with the sequence of numbers known and studied by Euler.