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  2. Generalizations of Fibonacci numbers - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of...

    A repfigit, or Keith number, is an integer such that, when its digits start a Fibonacci sequence with that number of digits, the original number is eventually reached. An example is 47, because the Fibonacci sequence starting with 4 and 7 (4, 7, 11, 18, 29, 47) reaches 47. A repfigit can be a tribonacci sequence if there are 3 digits in the ...

  3. Recurrence relation - Wikipedia

    en.wikipedia.org/wiki/Recurrence_relation

    A famous example is the recurrence for the Fibonacci numbers, = + where the order is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients , because the coefficients of the linear function (1 and 1) are constants that do not depend on n . {\displaystyle n.}

  4. Overlapping subproblems - Wikipedia

    en.wikipedia.org/wiki/Overlapping_subproblems

    Therefore, the computation of F(n − 2) is reused, and the Fibonacci sequence thus exhibits overlapping subproblems. A naive recursive approach to such a problem generally fails due to an exponential complexity. If the problem also shares an optimal substructure property, dynamic programming is a good way to work it out.

  5. Recursion (computer science) - Wikipedia

    en.wikipedia.org/wiki/Recursion_(computer_science)

    Multiple recursion can sometimes be converted to single recursion (and, if desired, thence to iteration). For example, while computing the Fibonacci sequence naively entails multiple iteration, as each value requires two previous values, it can be computed by single recursion by passing two successive values as parameters.

  6. Dynamic programming - Wikipedia

    en.wikipedia.org/wiki/Dynamic_programming

    For example, consider the recursive formulation for generating the Fibonacci sequence: F i = F i−1 + F i−2, with base case F 1 = F 2 = 1. Then F 43 = F 42 + F 41, and F 42 = F 41 + F 40. Now F 41 is being solved in the recursive sub-trees of both F 43 as well as F 42. Even though the total number of sub-problems is actually small (only 43 ...

  7. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two numbers that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers , commonly denoted F n .

  8. Fibonacci polynomials - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_polynomials

    In mathematics, the Fibonacci polynomials are a polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in a similar way from the Lucas numbers are called Lucas polynomials .

  9. Constant-recursive sequence - Wikipedia

    en.wikipedia.org/wiki/Constant-recursive_sequence

    The Fibonacci sequence is constant-recursive: each element of the sequence is the sum of the previous two. Hasse diagram of some subclasses of constant-recursive sequences, ordered by inclusion In mathematics , an infinite sequence of numbers s 0 , s 1 , s 2 , s 3 , … {\displaystyle s_{0},s_{1},s_{2},s_{3},\ldots } is called constant ...