India TST:Day 2 Problem 3
Source: medium
May 16, 2009
functioncombinatorics proposedcombinatorics
Problem Statement
Prove The Following identity:
\sum_{j \equal{} 0}^n \left ({3n \plus{} 2 \minus{} j \choose j}2^j \minus{} {3n \plus{} 1 \minus{} j \choose j \minus{} 1}2^{j \minus{} 1}\right ) \equal{} 2^{3n}.
The Second term on left hand side is to be regarded zero for j=0.