A well-behaved cousin of the Hofstadter sequence
Let \(T(n)\) be a sequence of integers, defined by the recursion \(T(n)=T(n- 1-T(n-1))+T(n-2-T(n-2))\) for \(n>2\) with \(T(0)=T(1)=T(2)=1\). The treatment of the sequences similar than this is hard in general, as we know very little about them. So the results about the sequence \(T(n)\) obtained in the present paper are very interesting. Among others the author proves that \(T(n+1)=T(n)\) or \(T(n)+1\) for any \(n>0\); there are exactly \(x+2\) consecutive integers \(n\) for which \(T(n)=2^ x\); furthermore \(T(n)/n\to 1/2\) as \(n\to\infty\).
scientific article; zbMATH DE number 94360