2025/04/14 by Tekcan, Ahmet
#11B37 #11B39 #11D09 #11D79 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.10152
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.