The two recursive sequences U_n | = | m U_(n - 1) + U_(n - 2) V_n | = | m V_(n - 1) + V_(n - 2) with U_0 = 0, U_1 = 1 and V_0 = 2, V_1 = m, can be solved for the individual U_n and V_n. They are given by U_n | = | (α^n - β^n)/Δ V_n | = | α^n + β^n, where Δ | congruent | sqrt(m^2 + 4) α | congruent | (m + Δ)/2 β | congruent | (m - Δ)/2.

Binet's formula | Fibonacci Q-matrix | Lucas sequence