In 1976, H. Hosoya of Ochanomizu University, Tokyo, introduced an interesting triangular array H; see Figure 15.1 [332]. 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, c015-math-001.

Image described by caption and surrounding text.

Figure 15.1 Hosoya's triangle H.


We can define the array H recursively, where c015-math-002 denotes the element in row n and column j:

15.2 equation

where c015-math-005 and c015-math-006.

Since , where and , it ...

Get Fibonacci and Lucas Numbers with Applications, Volume 1, 2nd Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.