For the sequence 1,2,5,14,41,122, I didn't notice that you gained each new term by multiplying by three and then subtracting one. However, the pattern I did notice is each additional term is obtained by adding 3^(n-1) where n is the term number. 1 + 3^0 = 2. 2 + 3^1 = 5. 5 + 3^2 = 14. Since these two methods provide the same result, they are probably related somehow, but I can't seem to figure it out.