In 1976, H. Hosoya of Ochanomizu University, Tokyo, introduced an interesting triangular array H; see Figure 15.1 . It is closely linked to Fibonacci numbers. We call it Hosoya's triangle. The array is symmetric about the vertical line through the middle, and the top two northeast and southeast diagonals consist of Fibonacci numbers. We can obtain every interior element by adding the two immediate neighbors along the northeast and northwest diagonals; for example, .
15.1 RECURSIVE DEFINITION
We can define the array H recursively, where denotes the element in row n and column j:
where and .
Since , where and , it ...