OEIS A000285: Pseudofibonacci numbers

Explore A000285, the Fibonacci-like sequence with seeds 1 and 4: A0=1, A1=4, An=An-1+An-2. We'll show how it relates directly to Fibonacci and Lucas numbers (A_n = F_n + L_n + 1, or A_n = 2F_n + F_{n+2}), and why this small seed change creates a distinct, richly connected family. We’ll highlight striking properties—only squares are 1, 4, 9 (and A_{-9}=81 for negative indices), and no term is ever twice a square—and reveal a combinatorial tiling interpretation and its appearance in the 4-1 Pascal triangle. A fun tour of how tweaking initial conditions opens new mathematical worlds in OEIS.

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