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Home » Stop Accidental Deletions! Master the Ultimate Linux Dir Delete Shortcut (Must Read Now) - ECD Germany

Stop Accidental Deletions! Master the Ultimate Linux Dir Delete Shortcut (Must Read Now) - ECD Germany

📅 May 6, 2026 👤 scraface

May 06, 2026

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Use states:
$S_n$: number of valid strings of length $n$ ending in 3
$T_n$: ending in exactly one 2 (i.e., last is 2, previous ≠ 2)
$U_n$: ending in exactly two consecutive 2s (i.e., last two are 22, bu...
Recurrences:
$S_n = S_{n-1} + T_{n-1} + U_{n-1}$ (append 3 to any valid string)
$T_n = S_{n-1}$ (append 2 to a string ending in 3)
$U_n = T_{n-1}$ (append 2 to a string ending in exactly one 2)
Initial conditions ($n=1$):
$S_1 = 1$ (string: 3)

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