Exact closed-form formulas are derived for the number of non-negative integer solutions to F_i x + F_{i+1} y + F_{i+2} z = n and the analogous Lucas equation.
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The Number of Solutions to $ax+by+cz=n$ for Fibonacci and Lucas triplets
Exact closed-form formulas are derived for the number of non-negative integer solutions to F_i x + F_{i+1} y + F_{i+2} z = n and the analogous Lucas equation.