OEIS A00044: Fibonacci with mortality (12-month lifespan)

We explore A00044, the Fibonacci-with-death model where rabbits live 12 months and then die, yielding the recurrence a(n) = a(n-1) + a(n-2) − a(n−13). The first dozen terms match Fibonacci, but mortality changes the long-run behavior while the golden ratio still surfaces as a limiting ratio. We'll unpack Michael Somos's elegant generating function, and the surprising combinatorial interpretation of A00044 as the number of ordered compositions of integers using odd numbers from 1 to 11, linking population dynamics to number theory and beyond.

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