Marinada '26

[lang=hr] Niz $a_n$ zadovoljava jednadžbu $$a_{m+n} + a_{m-n} = \frac{1}{2}(a_{2m} + a_{2n}), \quad \text{za } m \ge n \ge 0$$ Ako je $a_1 = 1$, odrediti $a_{2026}$. [/lang] [lang=en] The sequence $a_n$ satisfies the equation $$a_{m+n} + a_{m-n} = \frac{1}{2}(a_{2m} + a_{2n}), \quad \text{for } m \ge n \ge 0$$ If $a_1 = 1$, find $a_{2026}$. [/lang]