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PERRIN SEQUENCE IN C++ LANGUAGE



AMRUHA AHMED
6th October,2023.


The Perrin Sequence, also known as the Skiponacci Sequence, is an integer sequence whose n’th term abides by the following recurrence relation :
P(N)=P(N-2)+P(N-3)
Where P(0)=3, P(1)=0 and P(2)=2 are the initial conditions.

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VARIABLES REQUIRED:



ALGORITHM:


PROGRAM:

                
                    #include<iostream>
                    using namespace std;
                    int main()
                    {
                        int p0=3;//first term of the sequence
                        int p1=0;//second term of the sequence
                        int p2=2;//third term of the sequence
                        int pn;//n'th term of the sequence
                        int n;//number of terms to be displayed on the screen
                        int ctr=3;//number of terms displayed currently
                        cout<<"Enter the number of terms:"; 
                        cin>>n;
                        cout<<"The Perrin Sequence is ....\n";
                        cout<<p0<<"\t"<<p1<<"\t"<<p2;
                        pn=p1+p0;//p(n)=p(n-2)+p(n-3)
                        while(ctr<n)
                            {
                                //displaying n'th term
                                cout<<"\t"<<pn;
                                //updating the terms of the sequence for the next iteration
                                p0=p1;
                                p1=p2;
                                p2=pn;
                                pn=p0+p1;
                                // updating ctr value
                                ctr++;
                                
                            }
                        return 0;
                    }
                     

             
         
CODE COPIED

DRY RUN:

Supposing the input of number limit that is 'n' is provided as 6 then the values of p0,p1,p2 and pn will be as follows:


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The loop ceases when ctr becomes greater than or equal to n.


OUTPUT:

Enter the number of terms:6

The Perrin Sequence is ....

3 0 2 3 2 5