Gaussian Generalized Guglielmo Numbers
Bahadır Yılmaz
Department of Mathematics, Faculty of Science, Zonguldak B¨ ulent Ecevit University, 67100, Zonguldak, Turkey.
Yüksel Soykan *
Department of Mathematics, Faculty of Science, Zonguldak B¨ ulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this study, we define Gaussian generalized Guglielmo numbers in detail, and focus on four specific cases: Gaussian triangular numbers, Gaussian triangular-Lucas numbers, Gaussian oblong numbers, and Gaussian pentagonal numbers. In addition, we present some identities and matrices related to these sequences, as well as recurrence relations, Binet’s formulas, generating functions, Simpson’s formulas, and summation formulas.
Keywords: Gaussian triangular numbers, Gaussian oblong numbers, Gaussian pentegonal numbers, triangular numbers, oblong numbers, pentegonal numbers