"Lucas number" meaning in English

{
  "etymology_text": "Named after the mathematician François Édouard Anatole Lucas.",
  "forms": [
    {
      "form": "Lucas numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Lucas number (plural Lucas numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "Any member of an integer sequence that has the same recursive relationship as the Fibonacci sequence, i.e. each term is the sum of the two previous terms, but with different starting values such that the ratios of successive terms approach the golden ratio."
      ],
      "id": "en-Lucas_number-en-noun-k0Pp4ocj",
      "links": [
        [
          "integer",
          "integer"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "recursive",
          "recursive"
        ],
        [
          "relationship",
          "relationship"
        ],
        [
          "Fibonacci sequence",
          "Fibonacci sequence"
        ],
        [
          "ratio",
          "ratio"
        ],
        [
          "golden ratio",
          "golden ratio"
        ]
      ],
      "related": [
        {
          "word": "Lucas sequence"
        }
      ],
      "wikipedia": [
        "Lucas number"
      ]
    }
  ],
  "word": "Lucas number"
}

{
  "etymology_text": "Named after the mathematician François Édouard Anatole Lucas.",
  "forms": [
    {
      "form": "Lucas numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Lucas number (plural Lucas numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Lucas sequence"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys"
      ],
      "glosses": [
        "Any member of an integer sequence that has the same recursive relationship as the Fibonacci sequence, i.e. each term is the sum of the two previous terms, but with different starting values such that the ratios of successive terms approach the golden ratio."
      ],
      "links": [
        [
          "integer",
          "integer"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "recursive",
          "recursive"
        ],
        [
          "relationship",
          "relationship"
        ],
        [
          "Fibonacci sequence",
          "Fibonacci sequence"
        ],
        [
          "ratio",
          "ratio"
        ],
        [
          "golden ratio",
          "golden ratio"
        ]
      ],
      "wikipedia": [
        "Lucas number"
      ]
    }
  ],
  "word": "Lucas number"
}