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The tribonacci numbers are like the Fibonacci numbers, but instead of starting with two predetermined terms, the sequence starts with three predetermined terms and each term afterwards is the sum of the preceding three terms. The first few tribonacci numbers are:
This sequence of numbers of parents is the Fibonacci sequence. The number of ancestors at each level, F n, is the number of female ancestors, which is F n−1, plus the number of male ancestors, which is F n−2. [90] [91] This is under the unrealistic assumption that the ancestors at each level are otherwise unrelated.
Let k be defined as an element in F, the array of Fibonacci numbers. n = F m is the array size. If n is not a Fibonacci number, let F m be the smallest number in F that is greater than n. The array of Fibonacci numbers is defined where F k+2 = F k+1 + F k, when k ≥ 0, F 1 = 1, and F 0 = 1. To test whether an item is in the list of ordered ...
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers
In mathematics and computing, Fibonacci coding is a universal code [citation needed] which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end.
The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. [3] The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349 ...
where F n is the n th Fibonacci number. Such a sum is called the Zeckendorf representation of N. The Fibonacci coding of N can be derived from its Zeckendorf representation. For example, the Zeckendorf representation of 64 is 64 = 55 + 8 + 1. There are other ways of representing 64 as the sum of Fibonacci numbers 64 = 55 + 5 + 3 + 1 64 = 34 ...
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 .