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EXAMPLE
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a(1) = 1: [2].
a(2) = 4: [2,1,1], [2,2], [3,1], [4].
a(3) = 9: [2,2,1,1], [2,2,2], [3,1,1,1], [3,2,1], [3,3], [4,1,1], [4,2], [5,1], [6].
a(4) = 19: [2,2,1,1,1,1], [2,2,2,1,1], [2,2,2,2], [3,2,1,1,1], [3,2,2,1], [3,3,1,1], [3,3,2], [4,1,1,1,1], [4,2,1,1], [4,2,2], [4,3,1], [4,4], [5,1,1,1], [5,2,1], [5,3], [6,1,1], [6,2], [7,1], [8].
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