Given a sequence (un) of positive integers generated by u1 = 1, u2 = a,un = aun-1 + bun-2(n > 3), define the generalized factorial by [n]! = u1u2...un and the generalized binomial coefficient by C(i,j) = [i + j]!/([i]![j]!)- Assume that the prime p does not divide b. Let r = min{n : p un}. Theorem (Asymptotic abundance of residues): #{(i, j)|0 o oo for p = 1,... ,p - 1. Theorem 2 (Fractal dimension): Let Sk = rpk. The Hausdorff dimension of n Uj j展开▼
