I have a function $f$ that I believe satisfies the following formula for all $n$ and for $0\leq m \leq n+1$ $$(2m^2+1)^{n} = \sum_{i=0}^{m}f(n,m-i)$$ I don't think it is relevant to my question to provide any other details. Is is enough to do a simple induction on $n$?
2026-04-07 16:12:27.1775578347
Is it enough to just use induction?
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