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Special function F(n)

Source: 1970 AHSME Problem 16

March 24, 2014
functionAMC

Problem Statement

If F(n)F(n) is a function such that F(1)=F(2)=F(3)=1F(1)=F(2)=F(3)=1, and such that F(n+1)=F(n)⋅F(n−1)+1F(n−2)F(n+1)=\dfrac{F(n)\cdot F(n-1)+1}{F(n-2)} for n≥3n\ge 3, then F(6)F(6) is equal to
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>3<spanclass=′latex−bold′>(C)</span>7<spanclass=′latex−bold′>(D)</span>11<spanclass=′latex−bold′>(E)</span>26<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>3\qquad<span class='latex-bold'>(C) </span>7\qquad<span class='latex-bold'>(D) </span>11\qquad <span class='latex-bold'>(E) </span>26
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