Question

A person communicates over a channel in Morse Code, which consists of dashes and dots. It takes 1 millisecond to send a dot and 3 milliseconds to send a dash. There is no gap between consecutive symbols. Write a recurrence and initial conditions for the number of different sequences of dashes and dots that can be sent in n milliseconds.

Answer 1

For this question, the formula is:
f(n) = f(n - 1) + f(n - 3), for all n >= 3
f(n) = 1, for n <= 2

for n = 1 and n = 2, we only have 1 way that is all ones.
for n > 2, we can use 3 as well as 1, so number of ways is a combination of 1's and 3's.
The above recursion gives the result.

Hope this helps. Please rate the answer if you like it.