Three-term recurrence relation

In mathematics, and especially in numerical analysis, a homogeneous linear three-term recurrence relation (TTRR, the qualifiers "homogeneous linear" are usually taken for granted) is a recurrence relation of the form

${\displaystyle y_{n+1}=a_{n}y_{n}+b_{n}y_{n-1}}$ for ${\displaystyle n=1,2,...,}$

where the sequences ${\displaystyle \{a_{n}\}}$ and ${\displaystyle \{b_{n}\}}$, together with the initial values ${\displaystyle y_{0},y_{1}}$ govern the evolution of the sequence ${\displaystyle \{y_{n}\}}$.