OEMO 2001 Advanced Q4: Upper Secondary Mathematics Competition Question

Let A₀ = {1, 2} and for n > 0 let A_n be the set of all numbers that are either elements of A_n-1 or can be represented as the sum of two distinct elements of A_n-1.

Further let a_n = |A_n| be the number of elements of A_n.

Determine a_n as a function of n.

[OEMO 2001 Advanced Q4]

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