Abstract:
This article presents a new sequence called the Trilucas sequence. The discovery of
the Trilucas sequence is based on using the same recursive formula as the Tribonacci
sequence with the rst 3 terms of the Trilucas sequence taken from the rst 3 terms of
the Lucas sequence. From the Trilucas sequence, the Binet formula, the properties,
and the resulting residual sequence of the Trilucas sequence will be presented. The
properties that have been found will then be proven using the strong induction
method.