{
  "id": "1009.3216",
  "version": "v1",
  "published": "2010-09-16T16:25:46.000Z",
  "updated": "2010-09-16T16:25:46.000Z",
  "title": "Generalized Compositions and Weighted Fibonacci Numbers",
  "authors": [
    "Milan Janjic"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted $r$-generalized Fibonacci number. A relationship between these two numbers will be derived. We shall thus obtain a generalization of the well-known formula connecting Fibonacci numbers with the binomial coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-16T16:25:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted fibonacci numbers",
      "generalized compositions",
      "natural number",
      "well-known formula connecting fibonacci numbers",
      "generalized fibonacci number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.3216J"
    }
  }
}