On complex Leonardo numbers

被引:11
作者
Karatas, Adnan [1 ]
机构
[1] Pamukkale Univ, Dept Math, Fac Arts & Sci, Denizli, Turkey
关键词
Complex numbers; Fibonacci sequence; Lucas sequence;
D O I
10.7546/nntdm.2022.28.3.458-465
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this study, we introduce the complex Leonardo numbers and give some of their properties including Binet formula, generating function, Cassini and d'Ocagne's identities. Also, we calculate summation formulas for complex Leonardo numbers involving complex Fibonacci and Lucas numbers.
引用
收藏
页码:458 / 465
页数:8
相关论文
共 13 条
[1]  
Akhtaruzzamna M., 2011, International Journal of Arts, V1, P1, DOI DOI 10.5923/J.ARTS.20110101.01
[2]  
Alp Y., 2021, KONURALP J MATH, V9, P183
[3]   Hybrid Leonardo numbers [J].
Alp, Yasemin ;
Kocer, E. Gokcen .
CHAOS SOLITONS & FRACTALS, 2021, 150
[4]  
Catarino P, 2020, ACTA MATH UNIV COMEN, V89, P75
[5]   A note on h(x) - Fibonacci quaternion polynomials [J].
Catarino, Paula .
CHAOS SOLITONS & FRACTALS, 2015, 77 :1-5
[6]   Quaternion Algebras and Generalized Fibonacci-Lucas Quaternions [J].
Flaut, Cristina ;
Savin, Diana .
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2015, 25 (04) :853-862
[7]   COMPLEX FIBONACCI NUMBERS AND FIBONACCI QUATERNIONS [J].
HORADAM, AF .
AMERICAN MATHEMATICAL MONTHLY, 1963, 70 (03) :289-&
[8]   Horadam Octonions [J].
Karatas, Adnan ;
Halici, Serpil .
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2017, 25 (03) :97-106
[9]   An investigation of application of the golden ratio and Fibonacci sequence in fashion design and pattern making [J].
Kazlacheva, Z. I. .
17TH WORLD TEXTILE CONFERENCE AUTEX 2017 - SHAPING THE FUTURE OF TEXTILES, 2017, 254
[10]  
KOSHY T., 2011, Math. Spectrum, V43, P125