Define the sequence {g_n} as follows:

• g₀ = 51
• g₁ = 348
• g_n = 5g_n-1 - 6g_n-2 + 207ⁿ for n 2

Prove that for n 0, g_n = 2ⁿ + 3ⁿ + 7ⁿ⁺².