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arXiv · 2504.10152

Neo balcobalancing numbers

Ahmet Tekcan
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Abstract

In this work, we defined neo balcobalancing numbers, neo Lucas-balcobalancing numbers, neo balcobalancers and neo Lucas-balcobalancers and derived the general terms of these numbers in terms of balancing numbers. Conversely we deduced the general terms of balancing, cobalancing, Lucas-balancing and Lucas-cobalancing numbers in terms of these numbers. We also deduced some relations on Binet formulas, recurrence relations, relationship with Pell, Pell-Lucas, triangular, square triangular numbers, Pythagorean triples and Cassini identities. We also formulate the sum of first $n$-terms of these numbers and obtained some formulas for the sums of Pell, Pell-Lucas, balancing and Lucas-cobalancing numbers in terms of these numbers.

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Ahmet Tekcan. 2025-04-14. Neo balcobalancing numbers. https://arxiv.org/abs/2504.10152

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