{
  "abstract": "We construct a five-parameter quadratic algebraic generating function whose coefficient sequence has prescribed initial Hankel determinants $(λ,m,r,η)$ and whose Hankel transform belongs to the Somos-4 family $A(1,τ)$. The construction starts from a Stieltjes continued fraction whose coefficients are generated by an alternating recurrence compatible with the Somos-4 relation. We derive an explicit quadratic equation for the resulting generating function and give the corresponding coefficient recurrence. A subtle feature of the construction is the nonuniqueness of a coefficient sequence determined solely by its ordinary Hankel transform. To select a canonical representative, we additionally prescribe the shifted Hankel determinants obtained from the same Somos-4 orbit advanced by two indices. This companion condition determines the odd and even Stieltjes coefficients separately and removes the remaining freedom in the continued-fraction representation. We also analyze the two algebraic branches at the origin, where they coalesce, and derive a desingularized recurrence for the coefficients. The resulting construction provides a direct algebraic generating-function realization of a general five-parameter family of Somos-4 Hankel transforms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15754",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Scheuerle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7h819rzjwd414.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15754",
  "fulltext_url": null,
  "id": "7h819rzjwd414",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15754",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213348114",
  "pdf_url": "https://arxiv.org/pdf/2609.15754",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7h819rzjwd414.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15754",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15754"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Direct Generation of a Somos-4 Sequence from an Algebraic Generating Function",
  "title_text": "Direct Generation of a Somos-4 Sequence from an Algebraic Generating Function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7h819rzjwd414",
  "venue": "arXiv",
  "versions": []
}