ÖMO 1983 Problem 4

The sequence $(x_n)_{n \in \mathbb{N}}$ is defined by $x_1=2, x_2=3,$ and

$x_{2m+1}=x_{2m}+x_{2m-1}$ for $m \ge 1;$ $x_{2m}=x_{2m-1}+2x_{2m-2}$ for $m \ge 2.$

Determine $x_n$ as a function of $n$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.