Gaussian Generalized Woodall Numbers
Orhan Eren
Department of Mathematics, Faculty of Science, Zonguldak B¨ ulent Ecevit University, 67100, Zonguldak, Turkey.
Yuksel 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 work, we define and investigate Gaussian generalized Woodall numbers in detail, and focus on four specific cases: Gaussian modified Woodall numbers, Gaussian modified Cullen numbers, Gaussian Woodall numbers, and Gaussian Cullen numbers. 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: Woodall numbers, Cullen numbers, Gaussian Woodall numbers, Gaussian Cullen numbers, Gaussian generalizedWoodall numbers, Gaussian modifiedWoodall numbers, Gaussian modified Cullen numbers