Let S={(x,y)∈Z2∣0≤x≤11,0≤y≤9}. Compute the number of sequences (s0,s1,...,sn) of elements in S (for any positive integer n≥2) that satisfy the following conditions:
∙s0=(0,0) and s1=(1,0),
∙s0,s1,...,sn are distinct,
∙ for all integers 2≤i≤n, si is obtained by rotating si−2 about si−1 by either 90o or 180o in the
clockwise direction.