Anita Das - A Combinatorial Approach to the Tanny Sequence

dmtcs:547 - Discrete Mathematics & Theoretical Computer Science, July 16, 2011, Vol. 13 no. 2 -
A Combinatorial Approach to the Tanny SequenceArticle

Authors: Anita Das 1

  • 1 Department of Computer Science and Automation [Bangalore]

The Tanny sequence T (i) is a sequence defined recursively as T(i) = T(i - 1 - T(i - 1)) + T(i - 2 - T(i - 2)), T(0) = T(1) = T(2) = 1. In the first part of this paper we give combinatorial proofs of all the results regarding T(i), that Tanny proved in his paper "A well-behaved cousin of the Hofstadter sequence", Discrete Mathematics, 105(1992), pp. 227-239, using algebraic means. In most cases our proofs turn out to be simpler and shorter. Moreover, they give a "visual" appeal to the theory developed by Tanny. We also generalize most of Tanny's results. In the second part of the paper we present many new results regarding T(i) and prove them combinatorially. Given two integers n and k, it is interesting to know if T(n) = k or not. In this paper we characterize such numbers.

Volume: Vol. 13 no. 2
Section: Combinatorics
Published on: July 16, 2011
Accepted on: June 9, 2015
Submitted on: May 29, 2009
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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