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Home » $S_n$: number of valid strings of length $n$ ending in 3 - Crankk.io

$S_n$: number of valid strings of length $n$ ending in 3 - Crankk.io

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Feb 27, 2026

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Adding them:
The denominator is:
\frac{2a^2 + 2b^2}{a^2 - b^2} = 3
Factor out 2 in the numerator:
\frac{2(a^2 + b^2)}{a^2 - b^2} = 3
\frac{a^2 + b^2}{a^2 - b^2} = \frac{3}{2}
Question: Let $ g(x^2 + 1) = x^4 + 2x^2 + 2 $. Find $ g(x^2 - 1) $.
g(x^2 + 1) = x^4 + 2x^2 + 2
Let’s express the right-hand side in terms of $ x^2 + 1 $.
Let $ u = x^2 + 1 \Rightarrow x^2 = u - 1 $, so:

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