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Home » Staryu Unearthed: The Legendary Warrior You Won’t Believe Existed! - Baxtercollege

Staryu Unearthed: The Legendary Warrior You Won’t Believe Existed! - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \mathbf{v} imes \mathbf{a} = a(-4) - b(3) = -4a - 3b

📌 We set this equal to 5:

📌 -4a - 3b = 5

📌 This is a linear equation in two variables. We can express one variable in terms of the other. Solving for \(b\):

📌 -3b = 4a + 5 \quad \Rightarrow \quad b = -rac{4a + 5}{3}

📌 Thus, all vectors \(egin{bmatrix} a \ -rac{4a + 5}{3} \end{bmatrix}\) satisfy the condition.

📌 To write a specific solution, choose \(a = -1\):

📌 b = -rac{4(-1) + 5}{3} = -rac{-4 + 5}{3} = -rac{1}{3}

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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)
$U_n = T_{n-1}$ (append 2 to a string ending in exactly one 2)
Initial conditions ($n=1$):
$S_1 = 1$ (string: 3)
$T_1 = 1$ (2)
$U_1 = 0$ (can’t have two 2s)
Now compute step by step:
$n=2$:

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