Generalized Goggins’s Formula for Lucas and Companion Lucas Sequences

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In our previous papers, we have generalized Goggins’s formula given in [1] into two different directions [2] and [3]. In this paper, we shall give a more generalized formula which combine the results in [2] and those in [3]. Our formula (6) involves our previous results (4), (5) and also Goggins’s formula (1) as its special cases. Furthermore we shall give another formula (8) which is a generalization of a formula obtained in [2] too.

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