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Journal or Publication Title:
Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես
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Title:
A Note on Bi-Periodic Leonardo Sequence
Creator:
Catarino, P. M. M. ; Spreafico, E. V. P.
Contributor(s):
Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան
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Uncontrolled Keywords:
Leonardo Sequence ; Bi-Periodic Fibonacci Sequence ; Binet’s Formula ; Catalan’s Identity
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Abstract:
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 sequence{GLen}n≥0are studied and severalidentities, including the generating function and Binet’s formula,are established
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General note:
Electronic Open Access Publication of the National Academy of Sciences of Armenia