Stepping Beyond Fibonacci Numbers

Trying variants of a simple mathematical rule that yields interesting results can lead to additional discoveries and curiosities.

The numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55 belong to a famous sequence named for the Italian mathematician Fibonacci, who lived more than 700 years ago. Each consecutive number is the sum of the two numbers that precede it.