For n = p + f_{k1^2} + f_{k2^2}, the paper shows infinitely many n have zero representations and positive asymptotic densities have one or at least two representations.
Ding,On a problem of Romanoff type, Acta Arith
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On the sum of a prime and two Fibonacci numbers
For n = p + f_{k1^2} + f_{k2^2}, the paper shows infinitely many n have zero representations and positive asymptotic densities have one or at least two representations.