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Problem of the Week 936

Doubling Partitions

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In how many ways can we write 100 as a sum a1 +  a2 + ... + ak, where the ai are positive integers and ai is at least twice as big as ai-1? (note: k can possibly equal 1, 2, 3, ...)

Source: Suggested by John Renze (Northwestern); is related to Steenrod algebras, see: Steenrod, N. and Epstein, D., Cohomology Operations, Princeton University Press, 1962.
© Copyright 2001 Stan Wagon. Reproduced with permission.

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20 Apr 2001