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Omni-MATH / Pascal has a triangle. In the nth row, there are n+1 numbers a_(n,0),a_(n,1),a_(n,2),…,a_(n,n) where a_(n,0)=a_(n,n)=1. For all 1≤k≤n−1,a_(n,k)=a_(n−1,k)−a_(n−1,k−1). What is the s…

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problem

Pascal has a triangle. In the nnth row, there are n+1n+1 numbers an,0,an,1,an,2,…,an,na_{n, 0}, a_{n, 1}, a_{n, 2}, \ldots, a_{n, n} where an,0=an,n=1a_{n, 0}=a_{n, n}=1. For all 1≤k≤n−1,an,k=an−1,k−an−1,k−11 \leq k \leq n-1, a_{n, k}=a_{n-1, k}-a_{n-1, k-1}. What is the sum of all numbers in the 2018th row?
Plain-text mathematical notation (without MathML)
Pascal has a triangle. In the nth row, there are n+1 numbers a_(n,0),a_(n,1),a_(n,2),…,a_(n,n) where a_(n,0)=a_(n,n)=1. For all 1≤k≤n−1,a_(n,k)=a_(n−1,k)−a_(n−1,k−1). What is the sum of all numbers in the 2018th row?
Original LaTeX notation
Pascal has a triangle. In the $n$th row, there are $n+1$ numbers $a_{n, 0}, a_{n, 1}, a_{n, 2}, \ldots, a_{n, n}$ where $a_{n, 0}=a_{n, n}=1$. For all $1 \leq k \leq n-1, a_{n, k}=a_{n-1, k}-a_{n-1, k-1}$. What is the sum of all numbers in the 2018th row?

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Source and history

task_id
46e0242b-d2a6-55ba-a485-40507dab2460
task_key
test--46e0242b-d2a6-55ba-a485-40507dab2460
task_revision_id
1
config / split
/ test

Official source

initial import