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arXiv · 2610.00775

Riordan Arrays and Shifted Hankel Determinants of OEIS A005773

Daniel Yaqubi·Madjid Mirzavaziri
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Abstract

We study two Riordan arrays associated with the Motzkin-prefix sequence (\href{https://oeis.org/A005773}{OEIS A005773}). By connecting their production matrices through a simple boundary factorization, we obtain a period-three transformation on Motzkin endpoint distributions and exact formulas for paths by final height modulo~$3$. In addition, a unified factorization for the shifted Hankel matrices leads directly to explicit closed forms for the third and fourth Hankel determinants, $Δ_n^{(3)}$ and~$Δ_n^{(4)}$.

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Daniel Yaqubi, Madjid Mirzavaziri. 2026-09-30. Riordan Arrays and Shifted Hankel Determinants of OEIS A005773. https://arxiv.org/abs/2610.00775

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