Fibonacci sequence has been generalized in many ways. These termasuk:

• Generalizing index to negative integers to produce Neganombor Fibonacci.
• Generalizing index to real numbers using a modification of Binet's formula. [37]
• Starting with other integers. nombor Lucas have L1 = 1, L2 = 3, and Ln = Ln−1 + Ln−2. jujukan Primefree menggunakan Fibonacci recursion with other starting points in order to generate sequences in which all numbers are composite.
• Letting a number be a linear function (other than sum) of 2 preceding numbers. Nomber Pell mempunyai Pn = 2Pn – 1 + Pn – 2.
• Not adding immediately preceding numbers. Padovan sequence and nombor Perrin mempunyai P(n) = P(n – 2) + P(n – 3).
• Generating next number by adding 3 numbers (tribonacci numbers), 4 numbers (tetranacci numbers), or more.
• Adding other objects than integers, misalnya functions or strings -- one essential example is polinomial Fibonacci.