Talk:Linear recurrence with constant coefficients

Mathematics C‑class Low‑priority

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Clarify whether eventually-periodic sequences are allowed?

The article does not really clarify whether the following sequence: $1,0,0,0,0,0,...$ is a valid solution? According to the definition, it might be because it satisfies the following linear difference equation: $a_{0}=1,a_{1}=0,{\text{ and }}\forall t\in \mathbb {N} ,a_{t+2}=a_{t+1}+0a_{t}$ . This is consistent with the article saying that the equation holds for "the values of the elements of a sequence" (emphasis mine). Nothing is stated that $a_{n}$ must be nonzero. The page Constant-recursive sequence appears to allow eventually-periodic sequences.

However, it would not be allowed if the equation must hold for all $t\in \mathbb {Z}$ , rather than just $t\in \mathbb {N}$ . And my impression is that most of the results in the article (e.g., closed formula in powers of the characteristic roots) would not hold for eventually-periodic sequences. Caleb Stanford (talk) 18:51, 7 November 2021 (UTC)[reply]