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EXAMPLE
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a(3) = 2: [2,1], [1,2].
a(4) = 3: [2,1,1], [1,2,1], [1,1,2].
a(5) = 9: [3,2], [2,3], [2,2,1], [2,1,2], [1,2,2], [2,1,1,1], [1,2,1,1], [1,1,2,1], [1,1,1,2].
a(6) = 11: [2,2,1,1], [2,1,2,1], [2,1,1,2], [1,2,2,1], [1,2,1,2], [1,1,2,2], [2,1,1,1,1], [1,2,1,1,1], [1,1,2,1,1], [1,1,1,2,1], [1,1,1,1,2].
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