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Omni-MATH / For positive integers n, let the numbers c(n) be determined by the rules c(1)=1, c(2n)=c(n), and c(2n+1)=(−1)^(n)c(n). Find the value of ∑_(n=1)²⁰¹³c(n)c(n+2).

Problem

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problem

For positive integers nn, let the numbers c(n)c(n) be determined by the rules c(1)=1c(1) = 1, c(2n)=c(n)c(2n) = c(n), and c(2n+1)=(−1)nc(n)c(2n+1) = (-1)^n c(n). Find the value of ∑n=12013c(n)c(n+2). \sum_{n=1}^{2013} c(n) c(n+2).
Plain-text mathematical notation (without MathML)
For positive integers n, let the numbers c(n) be determined by the rules c(1)=1, c(2n)=c(n), and c(2n+1)=(−1)^(n)c(n). Find the value of ∑_(n=1)²⁰¹³c(n)c(n+2).
Original LaTeX notation
For positive integers $n$, let the numbers $c(n)$ be determined by the rules $c(1) = 1$, $c(2n) = c(n)$, and $c(2n+1) = (-1)^n c(n)$. Find the value of \[ \sum_{n=1}^{2013} c(n) c(n+2). \]

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Source and history

task_id
6b27b7af-03c2-572c-a888-9f24b028c6eb
task_key
test--6b27b7af-03c2-572c-a888-9f24b028c6eb
task_revision_id
1
config / split
/ test

Official source

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