![]() ![]() Which coincides for example with the number of independent vertex sets for cyclic graphs C n also have this property. The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. This produces a sequence where the ratios of successive terms approach the golden ratio, and in fact the terms themselves are roundings of integer powers of the golden ratio. Nice copy issued in wraps with a plastic comb spine. ![]() The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. Soft cover - Fibonacci Association, Houghton, Mifflin - 1969 - Condition: Good - Science. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences. The only triangular Lucas numbers are 1, 3, and 5778 (Ming 1991). Individual numbers in the Lucas sequence are known as Lucas numbers. The only square numbers in the Lucas sequence are 1 and 4 (Alfred 1964, Cohn 1964). The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. However, when its terms become very small, the arc's radius decreases rapidly from 3 to 1 then increases from 1 to 2. The Lucas spiral, made with quarter- arcs, is a good approximation of the golden spiral when its terms are large. ( December 2019) ( Learn how and when to remove this template message) Please help to improve this article by introducing more precise citations. This article includes a list of general references, but it lacks sufficient corresponding inline citations.
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