OEIS A00119: Representations of integers as sums of distinct Fibonacci numbers

We explore A00119, the count of ways to write an integer n as a sum of distinct Fibonacci numbers (with 1 treated as a separate Fibonacci value). We’ll unpack its defining recursion linked to A000119, examine the quasi-periodic patterns that appear, and connect these representations to the Fibonacci world and the golden ratio. We’ll also glance at the inverse sequence A083853 and how computational tools (like GP) help compute terms, situating A00119 within the rich web of OEIS Fibonacci representations.

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