A 7 Equation (A 6) can be simplified as ϕ g n − 1 = λ g n, A 8 where g n = f n − f n − 1.
To proceed further, we substitute (A 3) into (A 2): ( s n + λ + ϕ ) ( f n − s b n ) = ϕ ( f n − 1 − s b n − 1 ) + λ ( f n + 1 − s b n + 1 ).