A function may be partly defined in terms of itself. A familiar example is the Fibonacci number sequence: F(n) = F(n â 1) + F(n â 2). For such a definition to be useful, it must lead to values which are non-recursively defined, in this case F(0) = 0 and F(1) = 1.
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f(0) = 1
f(1) = 2
f(n+2) = f(n+1) +f(n)
A function may be partly defined in terms of itself. A familiar example is the Fibonacci number sequence: F(n) = F(n â 1) + F(n â 2). For such a definition to be useful, it must lead to values which are non-recursively defined, in this case F(0) = 0 and F(1) = 1.
In general for the fibonacci numbers, f(n) = f(n - 1) + f(n - 2)
So f(n + 2) = f(n + 1) + f(n)