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@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} }

- Published in SIAM J. Discrete Math. 2012
DOI:10.1137/100795425

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