id: 06585993
dt: j
an: 2016d.00605
au: Cereceda, José Luis
ti: Binet’s formula for generalized tribonacci numbers.
so: Int. J. Math. Educ. Sci. Technol. 46, No. 8, 1235-1243 (2015).
py: 2015
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: F65
ut: tribonacci numbers; generalized tribonacci sequence; characteristic
equation; Binet’s formula; symmetric function
ci:
li: doi:10.1080/0020739X.2015.1031837
ab: 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.
rv: