Triangular numbers and generalized fibonacci polynomial

Abstract In the present paper, we study triangular numbers. We focus on the linear homogeneous recurrence relation of degree 3 with constant coefficients for triangular numbers. Then we deal with the relationship between generalized Fibonacci polynomials and triangular numbers. We show that different properties of triangular numbers can be obtained by using this relationship. Finally, we examine the properties of the sequence A052529 that has strong relationships with triangular numbers.