The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation
F_n=F_(n-1)+F_(n-2) (1)
with F_1=F_2=1. As a result of the definition (1), it is conventional to define F_0=0.
The Fibonacci numbers for n=1, 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ... (Sloane's A000045).
Fibonacci numbers can be viewed as a particular case of the Fibonacci polynomials F_n(x) with F_n=F_n(1).
Fibonacci numbers are implemented in Mathematica as Fibonacci[n].
The Fibonacci numbers are also a Lucas sequence U_n(1,-1), and are companions to the Lucas numbers (which satisfy the same recurrence equation).
F_n=F_(n-1)+F_(n-2) (1)
with F_1=F_2=1. As a result of the definition (1), it is conventional to define F_0=0.
The Fibonacci numbers for n=1, 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ... (Sloane's A000045).
Fibonacci numbers can be viewed as a particular case of the Fibonacci polynomials F_n(x) with F_n=F_n(1).
Fibonacci numbers are implemented in Mathematica as Fibonacci[n].
The Fibonacci numbers are also a Lucas sequence U_n(1,-1), and are companions to the Lucas numbers (which satisfy the same recurrence equation).
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