Formulas for Fibonacci-Like Sequences Produced by Pascal-Like Triangles

Authors

Hiroshi Matsui, Kwansei Gakuin High School, Japan
Toshiyuki Yamauchi, Kwansei Gakuin High School, Japan

Abstract

In this paper we are going to present three formulas to express Fibonacci-like sequences with the Fibonacci sequence. We constructed Pascal-like triangles using probabilities of a game, and these Pascal-like triangles can be considered generalizations of the well known Pascal's triangle. Using these triangles, we can make Fibonacci-like sequences. We discovered an interesting formula for these Fibonacci-like sequences. We could generalize this formula, and got some interesting formulas that combine these Fibonacci-like sequences and the Fibonacci-sequence. These formulas can reveal very interesting relationships between Fibonacci-like sequences and the Fibonacci sequence, and we can expect a rich possibility of the research from these Fibonacci-like sequences.

Author Bio

The authors of the paper are Hiroshi Matsui and Toshiyuki Yamauchi who are 12 grade students. Their dream is to be scientists, and H.Matsui loves chemistry and T.Yamauchi loves physics, and both of them love computer languages such as Mathematica, Java and C++ .They discovered the theorems in this paper when they were studying mathematics using Mathematica.

The authors of the paper are Hiroshi Matsui and Toshiyuki Yamauchi who are 12 grade students. Their dream is to be scientists, and H.Matsui loves chemistry and T.Yamauchi loves physics, and both of them love computer languages such as Mathematica, Java and C++ . They discovered the theorems in this paper when they were studying mathematics using Mathematica.

Faculty Sponsor

Ryohei Miyadera

Recommended Citation

Matsui, Hiroshi and Yamauchi, Toshiyuki (2008) "Formulas for Fibonacci-Like Sequences Produced by Pascal-Like Triangles," Rose-Hulman Undergraduate Mathematics Journal: Vol. 9: Iss. 2, Article 14.
Available at: https://scholar.rose-hulman.edu/rhumj/vol9/iss2/14