If we apply the formula to As well as the Fibonacci numbers, other constant-recursive sequences include the Lucas numbers and Lucas sequences, the Jacobsthal numbers, the Pell numbers and more generally the solutions to Pell's equation. Δ {\displaystyle x_{t}} 2 >> …

Papanicolaou, Vassilis, "On the asymptotic stability of a class of linear difference equations,", linear difference equations with polynomial coefficients, "Using generating functions to solve linear inhomogeneous recurrence equations", "Difference and Functional Equations: Exact Solutions", "Difference and Functional Equations: Methods", https://en.wikipedia.org/w/index.php?title=Recurrence_relation&oldid=974126369, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License, Any sequence satisfying the recurrence relation can be written uniquely as a linear combination of solutions constructed in part 1 as, This page was last edited on 21 August 2020, at 07:00. , c n endstream

An example of a recurrence relation is the logistic map: with a given constant r; given the initial term x0 each subsequent term is determined by this relation. A better algorithm is called binary search.

, this defines a unique sequence with /PTEX.InfoDict 14 0 R Different solutions are obtained depending on the nature of the roots: If these roots are distinct, we have the general solution, while if they are identical (when A2 + 4B = 0), we have.

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. %���� A recurrence relation is an equation that expresses each element of a sequence as a function of the preceding ones. a e + The number of comparisons will be given by. ( {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/35\/Solve-Recurrence-Relations-Step-1-Version-3.jpg\/v4-460px-Solve-Recurrence-Relations-Step-1-Version-3.jpg","bigUrl":"\/images\/thumb\/3\/35\/Solve-Recurrence-Relations-Step-1-Version-3.jpg\/aid1087578-v4-728px-Solve-Recurrence-Relations-Step-1-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"