When you spot the obvious pattern (powers of 2) and write the elegant solution, but your professor apparently spent their weekend deriving a polynomial formula that looks like it escaped from a cryptography textbook.
Both answers are technically correct. One takes 2 seconds to write. The other requires factoring a quartic polynomial and probably a sacrifice to the math gods. Your professor chose violence.
The real kicker? They're both valid closed forms. It's like showing up to a potluck with a sandwich while someone else brought a seven-layer molecular gastronomy deconstructed sandwich experience.
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