Some algebraic identities on quadra Fibona-Pell integer sequence

摘要

In this work, we define a quadra Fibona-Pell integer sequence W n = 3 W n − 1 − 3 W n − 3 − W n − 4 $W_{n}=3W_{n-1}-3W_{n-3}-W_{n-4}$ for n ≥ 4 $ngeq4$ with initial values W 0 = W 1 = 0 $W_{0}=W_{1}=0$ , W 2 = 1 $W_{2}=1$ , W 3 = 3 $W_{3}=3$ , and we derive some algebraic identities on it including its relationship with Fibonacci and Pell numbers.