Cassini's Identity
For F_n the nth Fibonacci number,
| F_(n-1)F_(n+1)-F_n^2=(-1)^n. |
This identity was also discovered by Simson (Coxeter and Greitzer 1967, p. 41; Coxeter 1969, pp. 165-168; Wells 1986, p. 62). It is a special case of Catalan's identity with r=1.
See also
d'Ocagne's Identity, Catalan's Identity, Fibonacci NumberExplore with Wolfram|Alpha
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References
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, 1969.Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., p. 41, 1967.Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, p. 12, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, 1986.Referenced on Wolfram|Alpha
Cassini's IdentityCite this as:
Weisstein, Eric W. "Cassini's Identity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CassinisIdentity.html