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  2. 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 .

  3. 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.

  4. Fibonacci search technique - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_search_technique

    Fibonacci search has an average- and worst-case complexity of O(log n) (see Big O notation). The Fibonacci sequence has the property that a number is the sum of its two predecessors. Therefore the sequence can be computed by repeated addition. The ratio of two consecutive numbers approaches the Golden ratio, 1.618... Binary search works by ...

  5. Bell number - Wikipedia

    en.wikipedia.org/wiki/Bell_number

    In this formula, the summation in the middle is the general form used to define the exponential generating function for any sequence of numbers, and the formula on the right is the result of performing the summation in the specific case of the Bell numbers.

  6. 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).

  7. Fibonacci - Wikipedia

    en.wikipedia.org/wiki/Fibonacci

    In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377.

  8. Fibonorial - Wikipedia

    en.wikipedia.org/wiki/Fibonorial

    Here the fibonorial constant (also called the fibonacci factorial constant [1]) is defined by = = (), where = and is the golden ratio. An approximate truncated value of C {\displaystyle C} is 1.226742010720 (see (sequence A062073 in the OEIS ) for more digits).

  9. Pisano period - Wikipedia

    en.wikipedia.org/wiki/Pisano_period

    Plot of the first 10,000 Pisano periods. In number theory, the nth Pisano period, written as π (n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats.