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PreprintCC BY 4.0arXiv

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, Δn(3) and~Δn(4).

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Cite

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BibTeX
@misc{yaqubi2026riordan,
  title = {{Riordan Arrays and Shifted Hankel Determinants of OEIS A005773}},
  author = {Daniel Yaqubi and Madjid Mirzavaziri},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00775},
  eprint = {2610.00775},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00775},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Riordan Arrays and Shifted Hankel Determinants of OEIS A005773
AU  - Daniel Yaqubi
AU  - Madjid Mirzavaziri
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00775
UR  - https://arxiv.org/abs/2610.00775
AB  - 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).
ER  -