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Omni-MATH / Fibonacci numbers are defined as follows: F₀=F₁=1,F_(n+2)=F_(n+1)+F_(n),n≥0. Let a_(n) be the number of words that consist of n letters 0 or 1 and contain no two letters 1 at dista…

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problem

Fibonacci numbers are defined as follows: F0=F1=1,Fn+2=Fn+1+Fn,n≥0F_0 = F_1 = 1, F_{n+2} = F_{n+1}+F_n, n \geq 0. Let ana_n be the number of words that consist of nn letters 00 or 11 and contain no two letters 11 at distance two from each other. Express ana_n in terms of Fibonacci numbers.
Plain-text mathematical notation (without MathML)
Fibonacci numbers are defined as follows: F₀=F₁=1,F_(n+2)=F_(n+1)+F_(n),n≥0. Let a_(n) be the number of words that consist of n letters 0 or 1 and contain no two letters 1 at distance two from each other. Express a_(n) in terms of Fibonacci numbers.
Original LaTeX notation
Fibonacci numbers are defined as follows: $F_0 = F_1 = 1, F_{n+2} = F_{n+1}+F_n, n \geq 0$. Let $a_n$ be the number of words that consist of $n$ letters $0$ or $1$ and contain no two letters $1$ at distance two from each other. Express $a_n$ in terms of Fibonacci numbers.

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task_id
5e6bc115-9c55-5b3d-9da6-f3eeb60f867e
task_key
test--5e6bc115-9c55-5b3d-9da6-f3eeb60f867e
task_revision_id
1
config / split
/ test

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