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EXAMPLE
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The a(1) = 1 through a(6) = 20 square partitions:
{{1}} {{2}} {{3}} {{4}} {{5}} {{6}}
{{1,1}} {{1,1,1}} {{2,2}} {{1},{4}} {{3,3}}
{{1},{2}} {{1},{3}} {{2},{3}} {{1},{5}}
{{1,1,1,1}} {{1},{1,3}} {{2,2,2}}
{{1},{1,2}} {{1},{2,2}} {{2},{4}}
{{2},{1,1}} {{2},{1,2}} {{1},{1,4}}
{{3},{1,1}} {{4},{1,1}}
{{1,1,1,1,1}} {{1},{1,1,3}}
{{1},{1,1,2}} {{1,1},{1,3}}
{{1,1},{1,2}} {{1},{1,2,2}}
{{2},{1,1,1}} {{1,1},{2,2}}
{{1,2},{1,2}}
{{1},{2},{3}}
{{2},{1,1,2}}
{{3},{1,1,1}}
{{1,1,1,1,1,1}}
{{1},{1,1,1,2}}
{{1,1},{1,1,2}}
{{1,2},{1,1,1}}
{{2},{1,1,1,1}}
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