ON LUCAS v-TRIANGLES

are well known. A list of such basic identities can be found in [3]. If A ^ ±1 or B ^ 1, then w1? s^,... are nonzero by [1], and so are vx = u2lul9 v2 = M4/M2, ... . In the case A = B 1, we noted in [1] that un = 0 o 31n. IF vw = 0, then uln = i/wvw = 0; hence, 31n and un = Q, which is impossible since v~Au = 4B (cf. [3]). Thus, v0,v1? v2,... are all nonzero. We set vw! = Ilo ^ regard an empty product as value 1. For n,k eN with n>k,wt define the Lucas v-triangle {£} as follows: