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Integers expressible as the sum of two terms in the sequence

Source: CentroAmerican 2004

December 10, 2010

algebra proposedalgebra

Problem Statement

Define the sequence

(a_n)

as follows:

a_0=a_1=1

and for

k\ge 2

a_k=a_{k-1}+a_{k-2}+1

. Determine how many integers between

1

and

2004

inclusive can be expressed as

a_m+a_n

with

m

and

n

positive integers and

m\not= n