Generating function in recurrence relation

RECURRENCE RELATION:

How to solve.

Prob. Find the generating function for the following numeric function
ar = 7.3r , r  0.

Sol.
Step 1: Let generating function be
A(z) = a0z0 + a1z1 + a2z2 + a3z3 +…………….

Step 2:
Using  ar = 7.3r,

Find,

a0 = 7.30  = 7

a1 = 7.3= 21

a2 = 7.32 = 63

a3 = 7.33 = 189

and so on.

Step 3:

Now use value of a0, a1, a2, a3,…. Found in step 2 in to Step 1.

Such that,

A(z) = 7z0 + 21z1 + 63z2 + 189z3 +…………….

        =  7(30z0 + 31z1 + 32z2 + 33z3 +……………..)

        =  7(1 – 3z)-1  Ans.


Points to note:

If
A(z) = 30z0 + 31z1 + 32z2 + 33z3 +…… 
Solution will be = (1 – 3z)-1

If
A(z) = 30z0 - 31z1 + 32z2 - 33z3 +…… 

Python Programming ↓ 👆
Java Programming ↓ 👆
JAVA EasyExamNotes.com covered following topics in these notes.
JAVA Programs
Principles of Programming Languages ↓ 👆
Principles of Programming Languages
EasyExamNotes.com covered following topics in these notes.

Practicals:
Previous years solved papers:
A list of Video lectures References:
  1. Sebesta,”Concept of programming Language”, Pearson Edu 
  2. Louden, “Programming Languages: Principles & Practices” , Cengage Learning 
  3. Tucker, “Programming Languages: Principles and paradigms “, Tata McGraw –Hill. 
  4. E Horowitz, "Programming Languages", 2nd Edition, Addison Wesley

    Computer Organization and Architecture ↓ 👆

    Computer Organization and Architecture 

    EasyExamNotes.com covered following topics in these notes.

    1. Structure of desktop computers
    2. Logic gates
    3. Register organization
    4. Bus structure
    5. Addressing modes
    6. Register transfer language
    7. Direct mapping numericals
    8. Register in Assembly Language Programming
    9. Arrays in Assembly Language Programming

    References:

    1. William stalling ,“Computer Architecture and Organization” PHI
    2. Morris Mano , “Computer System Organization ”PHI

    Computer Network ↓ 👆
    Computer Network

    EasyExamNotes.com covered following topics in these notes.
    1. Data Link Layer
    2. Framing
    3. Byte count framing method
    4. Flag bytes with byte stuffing framing method
    5. Flag bits with bit stuffing framing method
    6. Physical layer coding violations framing method
    7. Error control in data link layer
    8. Stop and Wait scheme
    9. Sliding Window Protocol
    10. One bit sliding window protocol
    11. A protocol Using Go-Back-N
    12. Selective repeat protocol
    13. Application layer
    References:
    1. Andrew S. Tanenbaum, David J. Wetherall, “Computer Networks” Pearson Education.
    2. Douglas E Comer, “Internetworking with TCP/IP Principles, Protocols, And Architecture",Pearson Education
    3. KavehPahlavan, Prashant Krishnamurthy, “Networking Fundamentals”, Wiley Publication.
    4. Ying-Dar Lin, Ren-Hung Hwang, Fred Baker, “Computer Networks: An Open Source Approach”, McGraw Hill.