Abstract
Given an integer base b ≥ 2, we investigate a multivariate b-ary polynomial analogue of Stern’s diatomic sequence which arose in the study of hyper b-ary representations of integers. We derive various properties of these polynomials, including a generating function and identities that lead to factorizations of the polynomials. We use some of these results to extend an identity of Courtright and Sellers on the b-ary Stern numbers \( \mathit s_{b(n)} \). We also extend a result of Defant and a result of Coons and Spiegelhofer on the maximal values of \( \mathit s_{b(n)} \) within certain intervals.
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