applications of second order recurrence relation formula

  1. 1.

    Recall that the Fibonacci sequenceMathworldPlanetmath satisfies the recurrence relation


    Thus, f0=1, A=1, and B=1. Therefore, the theorem yields the following formulaMathworldPlanetmathPlanetmath for the Fibonacci sequence:

  2. 2.

    Fix ( a prime p and define a sequenceMathworldPlanetmath s by sn=τ(pn), where τ denotes the Ramanujan tau functionDlmfPlanetmath. Recall that τ satisfies


    Thus, s0=1, A=τ(p), and B=-p11. Therefore, the theorem yields


    This formula is valid for all primes p and all nonnegative integers n.

Title applications of second order recurrence relation formula
Canonical name ApplicationsOfSecondOrderRecurrenceRelationFormula
Date of creation 2013-03-22 17:51:46
Last modified on 2013-03-22 17:51:46
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 8
Author Wkbj79 (1863)
Entry type Application
Classification msc 11A25
Classification msc 11F11
Classification msc 11B39
Classification msc 11B37
Classification msc 03D20
Related topic FibonacciSequence
Related topic RamanujanTauFunction