Nested Recurrence Relations with Conolly-like Solutions

@article{Erickson2012NestedRR,
  title={Nested Recurrence Relations with Conolly-like Solutions},
  author={Alejandro Erickson and Abraham Isgur and Bradley W. Jackson and Frank Ruskey and Stephen M. Tanny},
  journal={SIAM J. Discrete Math.},
  year={2012},
  volume={26},
  pages={206-238}
}
A non-decreasing sequence of positive integers is (α, β)-Conolly, or Conollylike for short, if for every positive integer m the number of times that m occurs in the sequence is α + βrm, where rm is 1 plus the 2-adic valuation of m. A recurrence relation is (α, β)-Conolly if it has an (α, β)-Conolly solution sequence. We discover that Conolly-like sequences often appear as solutions to nested (or meta-Fibonacci) recurrence relations of the form A(n) = ∑k i=1 A(n− si− ∑pi j=1 A(n− aij)) with… CONTINUE READING
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