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Could you solve in a bottom-up manner?

  • There is 1 way to score 0 points.
  • The permutations of scoring 1 point is equal to the permutations to score 0 points (since we can add a free throw).
  • The permutations to score 2 points is the sum of permutations to score 0 points (adding a 2 pointer) and 1 point (adding a free throw).
  • The permutations to score 3 points is the sum of permutations to score 0 points (adding a 3 pointer), 1 point (adding a 2 pointer), and 2 points (adding a free throw).

The solution should be able to handle (60).

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