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Agung Prabowo
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, Universitas Jenderal Soedirman, Purwokerto, Indonesia
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Journal : International Journal of Quantitative Research and Modeling

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On Generalization of Fibonacci, Lucas and Mulatu Numbers Agung Prabowo
International Journal of Quantitative Research and Modeling Vol 1, No 3 (2020)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (362.037 KB) | DOI: 10.46336/ijqrm.v1i3.65

Abstract

Fibonacci numbers, Lucas numbers and Mulatu numbers are built in the same method. The three numbers differ in the first term, while the second term is entirely the same. The next terms are the sum of two successive terms. In this article, generalizations of Fibonacci, Lucas and Mulatu (GFLM) numbers are built which are generalizations of the three types of numbers. The Binet formula is then built for the GFLM numbers, and determines the golden ratio, silver ratio and Bronze ratio of the GFLM numbers. This article also presents generalizations of these three types of ratios, called Metallic ratios. In the last part we state the Metallic ratio in the form of continued fraction and nested radicals.
Co-Authors agus sugandha Agus Sugandha Agustini Tripena Annisa Wulansari Audia Kirana Budi Pratikno Diah Paramita Amitarwati Diah Paramita Amitarwati Diah Paramita Amitarwati Diva Sabina Permatasari Glenn Brillian Putra Herman Fernando Guswanto, Bambang Hendriya Hanifah Nurrahmi Hasriati Hasriati Ihda Hasbiyati Jajang Jajang Jumadil Saputra Lisnawati Lisnawati Mashuri Mashuri Monica Dwi Kusumaningsih Mustafa Mamat Mustafa Mamat Nita Rulianah Nur Amel Fitriyan Nur Jannah Parameswari Sang Galuh Kamulyan Pramono Sidi Ratri Maharsi Silfina Nihayatul Islamiyyah Siti Rahmah Nurshiami slamet riyadi Slamet Riyadi Sukono Sukono Supriyanto Supriyanto Supriyanto Suroto Suroto Tri Ayu Mulyani Triyani Triyani Zalfa Diba Adzkia Zulfatul Mukarromah