Lucas sequence

One of certain constant-recursive integer sequences

In mathematics, the Lucas sequences U n ( P , Q ) {\displaystyle U_{n}(P,Q)} and V n ( P , Q ) {\displaystyle V_{n}(P,Q)} are certain constant-recursive integer sequences that satisfy the recurrence relation x n = P ⋅ x n − 1 − Q ⋅ x n − 2 {\displaystyle x_{n}=P\cdot x_{n-1}-Q\cdot x_{n-2}} where P {\displaystyle P} and Q {\displaystyle Q} are fixed integers. Although U n ( P , Q ) {\displaystyle U_{n}(P,Q)} and V n ( P , Q ) {\displaystyle V_{n}(P,Q)} satisfy the same recurrence relation, they differ on the values of their first two elements a...