On Integer Sequences Derived from Balanced k-ary trees
نویسنده
چکیده
This article investigates numerous integer sequences derived from two special balanced k-ary trees. Main contributions of this article are two fold. The first one is building a taxonomy of various balanced trees. The other pertains to discovering new integer sequences and generalizing existing integer sequences to balanced k-ary trees. The generalized integer sequence formulae for the sum of heights and depths of all nodes in a complete k-ary tree are given. The explicit integer sequence formula for the sum of heights of all nodes in a size balanced k-ary tree is also given. Key–Words: complete k-ary tree, integer sequence, null-balanced k-ary tree, size-balanced k-ary tree
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On Complete and Size Balanced k-ary Tree Integer Sequences
Discovering new integer sequences and generalizing the existing ones are important and of great interest. In this article, various balanced k-ary trees are first studied and their taxonomy is built. In particular, two systematic balanced k-ary trees, whose nth tree is determined by a certain algorithm, are identified, i.e., complete and sizebalanced k-ary trees. The integer sequences from the f...
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