Panholzer, Alois; Prodinger, Helmut Towards a more precise analysis of an algorithm to generate binary trees: A tutorial. (English) Zbl 0927.11006 Comput. J. 41, No. 3, 201-204 (1998). In connection with counting binary trees [see L. Xiang, C. Tang and K. Ushijima, Comput. J. 40, 278-291 (1997; Zbl 0885.68120)] the recursion \(g_{n,k}=g_{n-1,k-1}+2g_{n-1,k}+g_{n-1,k+1}+1\) occurred. In this note, the authors obtain an explicit formula and an explicit recursion for \(g_{n,0}\). They use these (rather complicated) formulae to obtain asymptotic results about \(g_{n,0}\). The proof uses the generating function of the sequence \((g_{n,0})\). Reviewer: Alexander Pott (Magdeburg) MSC: 11B37 Recurrences 05A15 Exact enumeration problems, generating functions 68Q25 Analysis of algorithms and problem complexity 68R10 Graph theory (including graph drawing) in computer science Keywords:binary tree; generating function; recurrence relation; asymptotic results Citations:Zbl 0885.68120 Software:gfun PDFBibTeX XMLCite \textit{A. Panholzer} and \textit{H. Prodinger}, Comput. J. 41, No. 3, 201--204 (1998; Zbl 0927.11006) Full Text: DOI Link