A Study on Hyperbolic Generalized Guglielmo Numbers
Bahadır Yılmaz *
Department of Mathematics, Faculty of Science Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey.
Yüksel Soykan
Department of Mathematics, Faculty of Science Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we introduce the generalized hyperbolic Guglielmo numbers. We delve into various specific instances, including hyperbolic triangular numbers, hyperbolic triangular-Lucas numbers, hyperbolic oblong numbers, and hyperbolic pentagonal numbers. We present Binet’s formulas, generating functions and summation formulas for these numbers. Furthermore, Catalan’s and Cassini’s identities and matrices associated with these sequences will be provided deeply.
Keywords: Triangular numbers, triangular-Lucas numbers, oblong numbers, pentegonal numbers, hyperbolic triangular numbers, hyperbolic triangular-Lucas numbers, hyperbolic oblong numbers, hyperbolic pentegonal numbers