[1] P. Catarino and A. Borges, On Leonardo Numbers, Acta Mathematica Universitatis Comenianae, Vol:89, No.1 (2019), 75–86.
[2] P. Catarino and A. Borges, A Note on Incomplete Leonardo Numbers, Integers, Vol:20 (2020).
[3] C. Kızılates, On the Quadra Lucas-Jacobsthal Numbers, Karaelmas Science and Engineering Journal, Vol:7, No.2 (2017), 619-621.
[4] E. G. Kocer, N. Tuglu and A. Stakhov, On the m extension of the Fibonacci and Lucas p numbers, Chaos, Solitons&Fractals, Vol:40, No.4 (2009), 1890–1906.
[5] Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley&Sons, 2001.
[6] A. G. Shannon, A Note On Generalized Leonardo Numbers, Notes on Number Theory and Discrete Mathematics, Vol:25, No. 3 (2019), 97-101.
[7] N. J. A. Sloane, The On-line Encyclopedia of Integers Sequences, The OEIS Foundation Inc., http.//oeis.org.
[8] R. R. Stone, General identities for Fibonacci and Lucas numbers with polynomial subscripts in several variables, Fibonacci Quarterly, Vol:13 (1975), 289-294.
[9] N. Tuglu, C. Kızılates and S. Kesim, On the harmonic and hyperharmonic Fibonacci numbers, Advances Difference Equations, Article number: 297 (2015).
[10] Vajda, S., Fibonacci and Lucas numbers and the Golden Section: Theory and Applications, Halsted Press,1989.
[11] R. P. M. Vieira, F. R. V. Alves and P. M. Catarino, Relacoes Bidimensiona is E Identidades Da Sequencia De Leonardo, Revista Sergipana de Matematica e Educacao Matematica, No. 2 (2019), 156-173.
In this paper, we consider the Leonardo numbers which is defined by Catarino and Borges. Using Binet's formula of this sequence, we obtain new identities of the Leonardo numbers. Also , we give relations among the Fibonacci, Lucas and Leonardo numbers. Finally, using the matrix representation of Leonardo numbers, we obtain some identities of Leonardo numbers.
[1] P. Catarino and A. Borges, On Leonardo Numbers, Acta Mathematica Universitatis Comenianae, Vol:89, No.1 (2019), 75–86.
[2] P. Catarino and A. Borges, A Note on Incomplete Leonardo Numbers, Integers, Vol:20 (2020).
[3] C. Kızılates, On the Quadra Lucas-Jacobsthal Numbers, Karaelmas Science and Engineering Journal, Vol:7, No.2 (2017), 619-621.
[4] E. G. Kocer, N. Tuglu and A. Stakhov, On the m extension of the Fibonacci and Lucas p numbers, Chaos, Solitons&Fractals, Vol:40, No.4 (2009), 1890–1906.
[5] Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley&Sons, 2001.
[6] A. G. Shannon, A Note On Generalized Leonardo Numbers, Notes on Number Theory and Discrete Mathematics, Vol:25, No. 3 (2019), 97-101.
[7] N. J. A. Sloane, The On-line Encyclopedia of Integers Sequences, The OEIS Foundation Inc., http.//oeis.org.
[8] R. R. Stone, General identities for Fibonacci and Lucas numbers with polynomial subscripts in several variables, Fibonacci Quarterly, Vol:13 (1975), 289-294.
[9] N. Tuglu, C. Kızılates and S. Kesim, On the harmonic and hyperharmonic Fibonacci numbers, Advances Difference Equations, Article number: 297 (2015).
[10] Vajda, S., Fibonacci and Lucas numbers and the Golden Section: Theory and Applications, Halsted Press,1989.
[11] R. P. M. Vieira, F. R. V. Alves and P. M. Catarino, Relacoes Bidimensiona is E Identidades Da Sequencia De Leonardo, Revista Sergipana de Matematica e Educacao Matematica, No. 2 (2019), 156-173.