IOM 2018, Блиц, английски — Задача 78

OLYMPIAD OF METROPOLISES. Moscow, September 3 · 3 септември 2018 г.

Условие

Let $F$-restricted composition of number $n$ be an ordered collection of positive Fibonacci numbers whose sum is $n$. Let $f(n)$ be the number of summands in all $F$-restricted compositions of number $n$. For example $f(3) = 8$, because $3 = 1 + 1 + 1 = 1 + 2 = 2 + 1 = 3$, and there are $3 + 2 + 2 + 1 = 8$ summands in total. You need to find $f(10)$.

Отговори

Решение

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Оригинал в Архива: blitz.pdf · официални решения: blitz-answers.pdf