Define the nth 'staircase' as a polyomino with the nth triangular number of squares arranged as a sort of right triangle with a staircase along its hypotenuse. Below is n=3

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A straight s polyomino is simply a straight line of s squares.

Find a formula for the minimum number of straight polyominoes from a collection of size 1, 2, ..., s needed to tile the nth staircase.

For example if s=2 and n=3 it takes 4 pieces.

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