The familiar Fibonacci sequence (Fn)=(1,1,2,3,5,8,…) is defined recursively as
F0=1, F1=1, Fn=Fn−1+Fn−2 for n≥2.
Interestingly, F25=121393 and F50=20365011074.
Now define a new sequence (Gn) as follows:
G0=1, G1=2, Gn=3Gn−1−Gn−2 for n≥2.
Determine G25 without using a calculator.