Unrestricted Tribonacci and Tribonacci-Lucas quaternions

被引：0

作者：

Kizilaslan, Gonca ^{[1
]}

Karabulut, Leyla ^{[2
]}

机构：

[1] Kirikkale Univ, Fac Sci & Arts, Dept Math, TR-71450 Kirikkale, Turkiye

[2] Grad Sch Nat & Appl Sci, Dept Math, TR-71450 Kirikkale, Turkiye

来源：

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2023年 / 29卷 / 02期

关键词：

Quaternion; Recurrences; Integer sequences; GENERALIZED QUATERNIONS; K-FIBONACCI; NUMBERS;

D O I：

10.7546/nntdm.2023.29.2.310-321

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a generalization of Tribonacci and Tribonacci-Lucas quaternions with arbitrary Tribonacci numbers and Tribonacci-Lucas numbers coefficients, respectively. We get generating functions and Binet's formulas for these quaternions. Furthermore, several sum formulas and a matrix representation are obtained.

引用

页码：310 / 321

页数：12

共 38 条

[11] Feng JS, 2011, ARS COMBINATORIA, V100, P73
[12] Quaternion Algebras and Generalized Fibonacci-Lucas Quaternions
Flaut, Cristina
Savin, Diana
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2015, 25 (04) : 853 - 862
[13] On Generalized Fibonacci Quaternions and Fibonacci-Narayana Quaternions
Flaut, Cristina
Shpakivskyi, Vitalii
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2013, 23 (03) : 673 - 688
[14] Girard P. R., 1984, European Journal of Physics, V5, P25, DOI 10.1088/0143-0807/5/1/007
[15] On quaternion-Gaussian Lucas numbers
Halici, Serpil
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (09) : 7601 - 7606
[16] On a generalization for fibonacci quaternions
Halici, Serpil
Karatas, Adnan
[J]. CHAOS SOLITONS & FRACTALS, 2017, 98 : 178 - 182
[17] On Complex Fibonacci Quaternions
Halici, Serpil
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2013, 23 (01) : 105 - 112
[18] On Fibonacci Quaternions
Halici, Serpil
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2012, 22 (02) : 321 - 327
[19] Horadam A.F., 1993, Ulam Q, V2, P23
[20] COMPLEX FIBONACCI NUMBERS AND FIBONACCI QUATERNIONS
HORADAM, AF
[J]. AMERICAN MATHEMATICAL MONTHLY, 1963, 70 (03) : 289 - &

← 1 2 3 4 →