If F(n) is a function such that F(1)=F(2)=F(3)=1, and such that F(n+1)=(F(n)F(n-1)+1)/(F(n-2)) for n≥3, then F(6) is equal to:

1970 AMC 12 Problem 16

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16.

F(n)

is a function such that

F(1)=F(2)=F(3)=1,

and such that

F(n+1)=\frac{F(n)F(n-1)+1}{F(n-2)}

for

n\ge3,

then

F(6)

is equal to:

2

3

7

11

26

Compute the terms one at a time beginning with

F(4)

Use the recurrence successively for

n=3,4,5

Applying the recurrence successively,

\begin{aligned} F(4)&=\frac{1\cdot1+1}{1}=2,\\ F(5)&=\frac{2\cdot1+1}{1}=3, \end{aligned}

and

F(6)=\frac{3\cdot2+1}{1}=7.

Therefore, the correct answer is C.