ON THREE CONSECUTIVE PAIRS OF LUCAS AND FIBONACCI NUMBERS CONNECTED TO PELL-LUCAS AND PELL POLYNOMIALS

In the present paper we connect three consecutive pairs of Lucas and Fibonacci numbers, namely, { ( L 3 n , F 3 n ) , ( L 3 n +1 , F 3 n +1 ) , ( L 3 n +2 , F 3 n +2 ) : n = 0 , 1 , 2 , 3 , ···} to Pell-Lucas and Pell polyno- mials, namely, P n ( x ) = 1 2 h x + p x 2 + 1 n + x − p x 2 + 1 n i and Q n ( x ) = 1 2 √ x 2 + 1 h x + p x 2 + 1 n − x − p x 2 + 1 n i . We workout some interesting combinatorial identities of X n = P n (2) , Y n = Q n (2) and the three consec- utive pairs of Lucas and Fibonacci numbers