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Omni-MATH / An [i]anti-Pascal[/i] triangle is an equilateral triangular array of numbers…

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problem

An [i]anti-Pascal[/i] triangle is an equilateral triangular array of numbers such that, except for the numbers in the bottom row, each number is the absolute value of the difference of the two numbers immediately below it. For example, the following is an anti-Pascal triangle with four rows which contains every integer from 11 to 1010. \[\begin{array}{ c@{\hspace{4pt}}c@{\hspace{4pt}} c@{\hspace{4pt}}c@{\hspace{2pt}}c@{\hspace{2pt}}c@{\hspace{4pt}}c } \vspace{4pt} & & & 4 & & & \\\vspace{4pt} & & 2 & & 6 & & \\\vspace{4pt} & 5 & & 7 & & 1 & \\\vspace{4pt} 8 & & 3 & & 10 & & 9 \\\vspace{4pt} \end{array}\] Does there exist an anti-Pascal triangle with 20182018 rows which contains every integer from 11 to 1+2+3+…+20181 + 2 + 3 + \dots + 2018? [i]
Plain-text mathematical notation (without MathML)
An [i]anti-Pascal[/i] triangle is an equilateral triangular array of numbers such that, except for the numbers in the bottom row, each number is the absolute value of the difference of the two numbers immediately below it. For example, the following is an anti-Pascal triangle with four rows which contains every integer from 1 to 10.
\[\begin{array}{
c@{\hspace{4pt}}c@{\hspace{4pt}}
c@{\hspace{4pt}}c@{\hspace{2pt}}c@{\hspace{2pt}}c@{\hspace{4pt}}c
} \vspace{4pt}
 & & & 4 & & &  \\\vspace{4pt}
 & & 2 & & 6 & &  \\\vspace{4pt}
 & 5 & & 7 & & 1 & \\\vspace{4pt}
 8 & & 3 & & 10 & & 9 \\\vspace{4pt}
\end{array}\]
Does there exist an anti-Pascal triangle with 2018 rows which contains every integer from 1 to 1+2+3+…+2018?

[i]
Original LaTeX notation
An [i]anti-Pascal[/i] triangle is an equilateral triangular array of numbers such that, except for the numbers in the bottom row, each number is the absolute value of the difference of the two numbers immediately below it. For example, the following is an anti-Pascal triangle with four rows which contains every integer from $1$ to $10$.
\[\begin{array}{
c@{\hspace{4pt}}c@{\hspace{4pt}}
c@{\hspace{4pt}}c@{\hspace{2pt}}c@{\hspace{2pt}}c@{\hspace{4pt}}c
} \vspace{4pt}
 & & & 4 & & &  \\\vspace{4pt}
 & & 2 & & 6 & &  \\\vspace{4pt}
 & 5 & & 7 & & 1 & \\\vspace{4pt}
 8 & & 3 & & 10 & & 9 \\\vspace{4pt}
\end{array}\]
Does there exist an anti-Pascal triangle with $2018$ rows which contains every integer from $1$ to $1 + 2 + 3 + \dots + 2018$?

[i]

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Source and history

task_id
1551d531-d776-5ca4-8ea7-eafd7164afee
task_key
test--1551d531-d776-5ca4-8ea7-eafd7164afee
task_revision_id
1
config / split
/ test

Official source

initial import