Abstract: 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 formal one is important to analyzing algorithms involving the popular d-heap data structures. Those derived from the later one is pervasive in analyzing divide and conquer algorithms. Numerous generalized and new formulae for existing and new integer sequences generated from the complete and size-balanced k-ary trees are given. Key–Words: complete k-ary tree, integer sequence, null-balanced k-ary tree, size-balanced k-ary tre
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