Funny Fibonacci

The familiar Fibonacci sequence (Fn)=(1,1,2,3,5,8,)(F_n) = (1, 1, 2, 3, 5, 8, \ldots) is defined recursively as F0=1, F1=1, Fn=Fn1+Fn2 for n2.F_0 = 1,\ F_1 = 1,\ F_n = F_{n-1} + F_{n-2}\ \text{for}\ n \geq 2. Interestingly, F25=121393F_{25} = 121\:393 and F50=20365011074F_{50} = 20\:365\:011\:074.

Now define a new sequence (Gn)(G_n) as follows: G0=1, G1=2, Gn=3Gn1Gn2 for n2.G_0 = 1,\ G_1 = 2,\ G_n = 3G_{n-1} - G_{n-2}\ \text{for}\ n \geq 2. Determine G25G_{25} without using a calculator.

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