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Cn is the number of monotonic lattice paths along the edges of a grid with n × n square cells, which do not pass above the diagonal. A monotonic path is one which starts in the lower left corner, finishes in the upper right corner, and consists entirely of edges pointing rightwards or upwards. Counting such paths is equivalent to counting Dyck words: X stands for "move right" and Y stands for "move up".

Visuals for maths
Visuals for maths
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Cn is the number of monotonic lattice paths along the edges of a grid with n × n square cells, which do not pass above the diagonal. A monotonic path is one which starts in the lower left corner, finishes in the upper right corner, and consists entirely of edges pointing rightwards or upwards. Counting such paths is equivalent to counting Dyck words: X stands for "move right" and Y stands for "move up".
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Encrypted messaging app Telegram has announced that it is rolling out a new update that gives users more ways to use new emojis to express how they are feeling -- with infinite reactions and emoji statuses. The company said that premium users can pick reactions from an infinite selection of custom emojis. To make choosing from thousands of emojis easier, they can now attach up to three reactions per message.

Cn is the number of monotonic lattice paths along the edges of a grid with n × n square cells

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