IN-TST 2009 Problem 6

Prove The Following identity: $\sum_{j = 0}^n \left ({3n + 2 - j \choose j}2^j - {3n + 1 - j \choose j - 1}2^{j - 1}\right ) = 2^{3n}$ . The Second term on left hand side is to be regarded zero for j=0.