An Analytical Study on Dual Generalized Guglielmo Numbers
Bahadir Yilmaz *
Department of Mathematics, Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
Yuksel Soykan
Department of Mathematics, Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this study, we investigate the generalized dual hyperbolic Guglielmo numbers and then various special cases are explored (including dual triangular numbers, dual triangular-Lucas numbers, dual oblong numbers, and dual pentagonal numbers). Binet's formulas, generating functions, and summation formulas for these numbers are presented. Additionally, Catalan's and Cassini's identities are provided, along with matrices associated with these sequences. Moreover, we give some identities and matrices related with these sequences.
Keywords: Triangular numbers, triangular-Lucas numbers, oblong numbers, pentegonal numbers, dual triangular numbers, dual triangular-Lucas numbers, dual oblong numbers, dual pentegonal numbers
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