4un+2-4un+1+un=0, u0=2, u1=3.
Let's find some terms.
4u2-4u1+u0=0, u2=(4u1-u0)/4=(12-2)/4=5/2.
4u3-4u2+u1=0, u3=(4u2-u1)/4=(10-3)/4=7/4.
4u4-4u3+u2=0, u4=(4u3-u2)/4=(7-5/2)/4=9/8.
So, so far we have: 2, 3, 5/2, 7/4, 9/8, ... which can be written:
1/½, 3/1, 5/2, 7/4, 9/8, ...
A pattern suggest itself: The numerators form a sequence of natural odd numbers, while the denominators form a sequence of powers of 2. So:
un=(2n+1)/2n-1. On this assumption, u5=11/16.
4u5-4u4+u3=0, u5=(4u4-u3)/4=(9/2-7/4)/4=11/16. This confirms un=(2n+1)/2n-1.