THE GENERALIZED TRIBONACCI NUMBERS WITH NEGATIVE SUBSCRIPTS

摘要

Generalized tribonacci numbers Rn are defined through the recurrence Rn+1 = aRn + bRn1 + cRn2. A generating matrix of three tribonacci sequences with negative subscripts is defined and used to establish identities connecting these sequences which is analogous to the matrix of Shannon and Horadam. We derive an explicit formula for the generalized tribonacci numbers with negative subscripts.