DISCRETE MATH

PLEASE FOLLOW THE INSTRUCTIONS AND PROVIDE STEP BY STEP FOR EACH SUB-QUESTION

Call a string of letters "legal" if it can be produced by concatenating (running together) copies of the following strings: 'v', 'ww', 'xxx' 'yyy' and ' zzz '. For each integer n1, let tn be the number of legal strings with n letters. For example, t1=1 (' v ' is the only the legal string). t2= tn=atn1+btn2+ctn3 for each integer n4 where a=b=, and c= For each integer n1, let pn be the number of legal strings with n letters that also read the same right to left as they do left to right (like ' xxxvxxx, for example). Which of the following expressions is equal to p101 ? t50+3t49t50+3t48p100+p99t50+t49p50+p49t100+t99p50+3p49t50+t48