Minimal path sets with known size in a consecutive-2-out-of-n:F system

K.G. Ramamurthy showed that the number of minimal path sets of a linear consecutive-2-out-of-n:F system is the rounded value of the expression ρⁿ(1 + ρ)²/(2ρ + 3) where ρ is the unique real root of the cubic equation x³ − x − 1 = 0. This paper gives two other formulae for the same. The first formula is in terms of the binomial coefficients, while the second formula is in terms of the number of minimal path sets with known size of a linear consecutive-2-out-of-n:F system. It is shown that the number of minimal path sets of a circular consecutive-2-out-of-n:F system is the rounded value of ρⁿ, for n ≥ 10.