On the number of gapped repeats with arbitrary gap

For any functions f(x), g(x) from N to R we call repeats uvu such that g(|u|)≤|v|≤f(|u|) as f,g-gapped repeats. We study the possible number of f,g-gapped repeats in words of fixed length n. For quite weak conditions on f(x), g(x) we obtain an upper bound on this number which is linear in n.