Problem: Compute the total number Sn of different Morse code messages (message=any string of dots and dashes) that can be sent in n time units? To solve this problem, complete the following steps:

1.Show that S1=1, S2=2, S3=3, S4=5 by just listing all of the possible messages in each case.

Question

Problem: Compute the total number Sn of different Morse code messages (message=any string of dots and dashes) that can be sent in n time units? To solve this problem, complete the following steps:

1.Show that S1=1, S2=2, S3=3, S4=5 by just listing all of the possible messages in each case.

anonymous · Answer

2.Explain why the following recurrence relation holds for Sn: 

                    Sn = Sn-1 + Sn-2 for n > 2 

             	3.Find a formula for Sn as a function of n; that is, solve the 	discrete  dynamical system: 

                    (I) S1 = 1, S2 = 2 
                    (R) Sn = Sn-1 + Sn-2 for n > 2