{
  "id": "2211.12637",
  "version": "v1",
  "published": "2022-11-22T23:52:28.000Z",
  "updated": "2022-11-22T23:52:28.000Z",
  "title": "Conjectures on Somos $4$, $6$ and $8$ sequences using Riordan arrays and the Catalan numbers",
  "authors": [
    "Paul Barry"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give conjectures on the form of families of integer sequences whose Hankel transforms are, respectively, $(\\alpha, \\beta)$ Somos $4$ sequences, $(\\alpha, 0, \\gamma)$ Somos $6$ sequences, and $(\\alpha, \\beta, \\gamma, \\delta)$ Somos $8$ sequences, for particular values of $\\alpha$, $\\beta$, $\\gamma$, $\\delta$ which we describe. The sequences involved can be described in terms of the application of certain stretched Riordan arrays to the Catalan numbers, accompanied by a (sequence) Hankel transform. The combination of Riordan array and the Catalan numbers results from the study of certain generalized Jacobi continued fractions, based on the Counting Automata Methodology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-22T23:52:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37",
      "05A15",
      "15B36",
      "11A55",
      "15A15",
      "15B05"
    ],
    "keywords": [
      "conjectures",
      "hankel transform",
      "catalan numbers results",
      "generalized jacobi continued fractions",
      "stretched riordan arrays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}