ON HORADAM-LUCAS SEQUENCE

Horadam introduced a generalized sequence of numbers, describing its key features and the special sub-sequences obtained from specific choices of initial parameters. This sequence and its sub-sequences are known as the Horadam, gener-alized Fibonacci, and generalized Lucas numbers, respectively. In the present study, we propose another new sequence, which satisfies a second-order recurrence relation. Further, we prove the Binet's formula, some famous identities, and summation for-mulas for this new sequence. In particular, we demonstrate the interrelationships between our new sequence and the Horadam sequence.