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EXAMPLE
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a(2) = 3: [1,1], [1,2], [2,1].
a(3) = 10: [1,1,1], [1,1,2], [1,1,3], [1,2,1], [1,2,2], [1,3,1], [2,1,1], [2,1,2], [2,2,1], [3,1,1].
a(4) = 31: [1,1,1,1], [1,1,1,2], [1,1,1,3], [1,1,1,4], [1,1,2,1], [1,1,2,2], [1,1,2,3], [1,1,3,1], [1,1,3,2], [1,1,4,1], [1,2,1,1], [1,2,1,2], [1,2,1,3], [1,2,2,1], [1,2,3,1], [1,3,1,1], [1,3,1,2], [1,3,2,1], [1,4,1,1], [2,1,1,1], [2,1,1,2], [2,1,1,3], [2,1,2,1], [2,1,3,1], [2,2,1,1], [2,3,1,1], [3,1,1,1], [3,1,1,2], [3,1,2,1], [3,2,1,1], [4,1,1,1].
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