$T_1 = 1$ (2)

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• $U_n = T_{n-1}$ (append 2 to a string ending in exactly one 2)
• Initial conditions ($n=1$):
• $S_1 = 1$ (string: 3)
• $U_1 = 0$ (can’t have two 2s)
• Now compute step by step:
• $n=2$:

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