OEIS A000128: Non-linear binomial sums and Fibonacci connections

We explore A000128, a deceptively simple sequence that begins 1, 2, 4, 8, 16, 31 and is classified as a non-linear binomial sum. We break down what a non-linear binomial sum means, show how it links to Fibonacci numbers, binomial coefficients, and recursion, and discuss its elegant generating function. Along the way we’ll see how differences tie it to related sequences and what these connections reveal about the broader web of number theory.

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