Its generating function has closed form "x over 1 minus x minus x squared" for "magnitude x less than 1 over phi" and Binet's formula gives a more explicit link to the Golden Ratio.
Donald Knuth claims Indian prosodists discovered this object while counting all 1 and 2 beat sequences with a fixed number of beats and he also used it in his polyphase sort. Zeckendorf's theorem represents the integers as a unique sum from its elements. Its generating function has closed form "x over 1 minus x minus x squared" for "magnitude x less than 1 over phi" and Binet's formula gives a more explicit link to the Golden Ratio. Phyllotaxis, or plant leaf arrangement, follows ratios occurring in, for 10 points, what integer sequence which begins 1, 1, 2, 3, 5, 8.
Donald Knuth claims Indian prosodists discovered this object while counting all 1 and 2 beat sequences with a fixed number of beats and he also used it in his polyphase sort.
{Fibonacci} sequence