On Generalized Bigollo Numbers
Yüksel Soykan *
Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey.
Inci Okumus
Department of Engineering Sciences, Faculty of Engineering, Istanbul University-Cerrahpasa, 34320 Istanbul, Turkey.
Nazmiye Gönül Bilgin
Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
It is aimed to describe generalized Bigollo sequences and to examine Bigollo and Bigollo-Lucas sequences in this article. For this purpose, we give Binet’s formulas, Simson formulas, generating functions and we introduce a lot of main features of these sequences. Also, we get some formulas and give special matrices for these generalized sequences. Finally, we have determined some close relationships between Bigollo and Bigollo-Lucas numbers and Mersenne, Mersenne-Lucas numbers.
Keywords: Mersenne numbers, bigollo numbers, bigollo-lucas numbers, mersenne-lucas numbers, tribonacci numbers