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Problem 15: Lattice paths

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

RRDD

RDRD

RDDR

DRRD

DRDR

DDRR

How many such routes are there through a 20×20 grid?

JavaScript

See the Pen Problem 15 by Joshua Bee (@JoshuaBee) on CodePen.