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Home / $U_n = T_{n-1}$ (append 2 to a string ending in exactly one 2)

$U_n = T_{n-1}$ (append 2 to a string ending in exactly one 2)

February 22, 2026

$$U_n = T_{n-1}$ (append 2 to a string ending in exactly one 2)$

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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)
Initial conditions ($n=1$):
$S_1 = 1$ (string: 3)
$T_1 = 1$ (2)

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