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EXAMPLE
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For n = 1, the a(1) = 1 solution is (1,1,1,1).
For n = 4, the a(4) = 28 solutions are (k,k,k,k) for k=1,2,3,4, the 12 permutations of (1,2,4,4) and the 12 permutations of (2,3,4,4).
For n = 40, the a(40) - a(39) = 289 new solutions are:
the 24 permutations of (4, 8, 10, 40),
the 12 permutations of (4, 10, 40, 40),
the 12 permutations of (5, 12, 40, 40),
the 24 permutations of (8, 10, 12, 40),
the 24 permutations of (8, 15, 20, 40),
the 12 permutations of (10, 16, 16, 40),
the 24 permutations of (10, 18, 24, 40),
the 12 permutations of (10, 20, 40, 40),
the 24 permutations of (12, 20, 24, 40),
the 24 permutations of (14, 24, 35, 40),
the 24 permutations of (15, 24, 30, 40),
the 12 permutations of (16, 16, 20, 40),
the 12 permutations of (20, 20, 24, 40),
the 12 permutations of (20, 30, 40, 40),
the 12 permutations of (24, 30, 30, 40),
the 12 permutations of (28, 35, 40, 40),
the 12 permutations of (30, 36, 40, 40),
and (40, 40, 40, 40).
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