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B4

Part of 1957 Putnam

Problems(1)

Putnam 1957 B4

Source: Putnam 1957

7/1/2022
Let a(n)a(n) be the number of representations of the positive integer nn as an ordered sum of 11's and 22's. Let b(n)b(n) be the number of representations of the positive integer nn as an ordered sum of integers greater than 1.1. Show that a(n)=b(n+2)a(n)=b(n+2) for each nn.
PutnamcombinatoricsrepresentationSummation