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  2. Dynamic programming - Wikipedia

    en.wikipedia.org/wiki/Dynamic_programming

    Using dynamic programming in the calculation of the nth member of the Fibonacci sequence improves its performance greatly. Here is a naïve implementation, based directly on the mathematical definition: function fib(n) if n <= 1 return n return fib(n − 1) + fib(n − 2)

  3. Wythoff array - Wikipedia

    en.wikipedia.org/wiki/Wythoff_array

    In mathematics, the Wythoff array is an infinite matrix of integers derived from the Fibonacci sequence and named after Dutch mathematician Willem Abraham Wythoff.Every positive integer occurs exactly once in the array, and every integer sequence defined by the Fibonacci recurrence can be derived by shifting a row of the array.

  4. Overlapping subproblems - Wikipedia

    en.wikipedia.org/wiki/Overlapping_subproblems

    For example, the problem of computing the Fibonacci sequence exhibits overlapping subproblems. The problem of computing the n th Fibonacci number F ( n ), can be broken down into the subproblems of computing F ( n − 1) and F ( n − 2), and then adding the two.

  5. Generalizations of Fibonacci numbers - Wikipedia

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

    A Fibonacci sequence of order n is an integer sequence in which each sequence element is the sum of the previous elements (with the exception of the first elements in the sequence). The usual Fibonacci numbers are a Fibonacci sequence of order 2.

  6. 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.}

  7. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    For Fibonacci numbers starting with F 1 = 0 and F 2 = 1 and with each succeeding Fibonacci number being the sum of the preceding two, one can generate a sequence of Pythagorean triples starting from (a 3, b 3, c 3) = (4, 3, 5) via

  8. Fibonacci coding - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_coding

    To encode an integer N: . Find the largest Fibonacci number equal to or less than N; subtract this number from N, keeping track of the remainder.; If the number subtracted was the i th Fibonacci number F(i), put a 1 in place i − 2 in the code word (counting the left most digit as place 0).

  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 ...