
06585993
j
2016d.00605
Cereceda, Jos\'e Luis
Binet's formula for generalized tribonacci numbers.
Int. J. Math. Educ. Sci. Technol. 46, No. 8, 12351243 (2015).
2015
Taylor \& Francis, Abingdon, Oxfordshire
EN
F65
tribonacci numbers
generalized tribonacci sequence
characteristic equation
Binet's formula
symmetric function
doi:10.1080/0020739X.2015.1031837
Summary: In this note, we derive Binet's formula for the general term $\mathcal{T}_n$ of the generalized tribonacci sequence. This formula gives $\mathcal{T}_n$ explicitly as a function of the index $n$, the roots of the associated characteristic equation, and the initial terms $\mathcal{T}_0$, $\mathcal{T}_1$, and $\mathcal{T}_2$. 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.