On the D(−1)-triple {1,k2+1,k2+2k+2} and its unique D(1)-extension

In this paper, we consider the D(−1)-triple {1,k2+1,2(k+1)+1}. We extend the result obtained by Dujella, Filipin, and Fuchs (2007) [13] by determining the D(−1)-extension of this set. Moreover, we obtain a D(1)-extension of the triple.