On triangles with coordinates of vertices from the terms of the sequences {u kn} and {vkn}

Abstract

In this paper, we determine some results of the triangles with coordinates of vertices involving the terms of the sequences {U-kn} and {V-kn} where U-kn are terms of a second order recurrent sequence and V-kn are terms in the companion sequence for odd positive integer k, generalizing works of Cerin. For example, the cotangent of the Brocard angle of the triangle Delta(kn) iscot(Omega(Delta kn)) = Uk(2n+3) V-2k - Vk(2n+3)Uk/(-1)U-n(2k).