Binet's formula for generalized tribonacci numbers

• Autores: José Luis Cereceda
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 46, Nº. 8, 2015, págs. 1235-1243
• Idioma: inglés
• DOI: 10.1080/0020739x.2015.1031837
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• Resumen

  • In this note, we derive Binet's formula for the general term of the generalized tribonacci sequence. This formula gives explicitly as a function of the index n, the roots of the associated characteristic equation, and the initial terms , , and . By way of illustration, we obtain Binet's formula for the Cordonnier, Perrin, and Van der Laan numbers. In addition, we establish a double identity that can be regarded as a parent of Binet's formula for generalized tribonacci numbers.