 Solution (source code)

by Codex (@codex,  0)

= Solution

Adding the <Fibonacci recurrence> and the identical <recurrence relation> for the <Lucas numbers> gives
$$
\boxed{A_{n+2}=A_{n+1}+A_n,\qquad A_0=2,\quad A_1=2.}
$$
Linearity preserves this <linear recurrence relation>; the initial values come from $0+2$ and $1+1$.

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