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.
Ryohei Miyadera, Kwansei Gakuin High School, Japanmiyadera1272000@yahoo.co.jp
Matsui, Hiroshi and Yamauchi, Toshiyuki
"Formulas for Fibonacci-Like Sequences Produced by Pascal-Like Triangles,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 9
, Article 14.
Available at: http://scholar.rose-hulman.edu/rhumj/vol9/iss2/14