The fibonacci series can be printed in the LMC in the following manner:
INP
STO n #number of terms
LDA one
OUT
loop LDA fib #THE MAIN LOOP THAT PRINTS FIBONACCI NUMBERS
STO temp2
ADD temp
STO fib
LDA temp2
STO temp
BR check
check LDA n #LOOP TO KEEP A TRACK OF NUMBER OF TERMS
BRZ halt
SUB one
STO n
BRZ halt
LDA fib
OUT
BR loop
halt HLT
n DAT 000
fib DAT 001
temp DAT 001
temp2 DAT 000
one DAT 001
Explanation: The program first asks for an input n, the number of terms to be printed.Then the loop starts running - it will print the default value of variable fib, which has been set to 1. The value of fib is stored in another variable temp2, and the variable temp is used to record the previous value of fib so that the numbers are added correctly and a correct sequence is obtained. The loop controls the values of fib, temp and temp2 as the number of terms are increased.
The program then checks if the number of terms required have been printed and decrements the value of n. If n=0 it means that the required number of terms has been reached and the program halts. If n is not zero, the loop continues till n=0.
**Though there might me more efficient methods, however this one works correctly and uses a pretty less number of mailboxes which makes it quite efficient.