Fast Path: F(0) to F(78)
Sequence Detection
BigInt Path: Beyond F(78)
Key Formulas
Gessel's Identity
N is Fibonacci ⟺ 5N² ± 4 is a perfect square
Lucas-Fibonacci Relationship
F(n-1) = (L(n) - F(n)) / 2
F(n+1) = F(n) + F(n-1)
F(n+1) = F(n) + F(n-1)
Golden Ratio Scoring
Score = cells × 10 + φ^(cells/5) × 100
φ = 1.618...
φ = 1.618...
Integer Square Root
Newton's Method for BigInt
x(n+1) = ⌊(x(n) + N/x(n)) / 2⌋
x(n+1) = ⌊(x(n) + N/x(n)) / 2⌋