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Show that the Catalan numbers also enumerate the number of tilings of a regular n-step staircase pattern with n rectangles (the tilings for n =
Show that the Catalan numbers also enumerate the number of tilings of a regular n-step staircase pattern with n rectangles (the tilings for n = 4 are shown on the next page). Do this either by showing it satisfies the recurrence relation, or through a bijection with another type of object for which it was shown in class that it is counted by the Catalan numbers
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