A Note on Bi-Periodic Leonardo Sequence - Catarino, P. M. M.; Spreafico, E. V. P.
n this work, we define a new generalization of theLeonardo sequence by the recurrence relationGLen=aGLen−1+GLen−2+a(for evenn) andGLen=bGLen−1+GLen−2+b(foroddn) with the initial conditionsGLe0= 2a−1 andGLe1=2ab−1, whereaandbare real nonzero numbers. Some algebraicproperties of the sequenceGLenn≥0are studied and severalidentities, including the generating function and Binet’s formula,are established
Keywords: Mathematics