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 Fibonacci

 http://functions.wolfram.com/04.11.16.0023.01

 Input Form

 Fibonacci[n]^2 == (1/5) (LucasL[2 n] - 2 (-1)^n) /; Element[n, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Fibonacci", "[", "n", "]"]], "2"], "\[Equal]", RowBox[List[FractionBox["1", "5"], RowBox[List["(", RowBox[List[RowBox[List["LucasL", "[", RowBox[List["2", "n"]], "]"]], "-", RowBox[List["2", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]]]], ")"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

 MathML Form

 F TagBox["F", Fibonacci] n 2 1 5 ( L TagBox["L", LucasL] 2 n - 2 ( - 1 ) n ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] Condition Fibonacci n 2 1 5 LucasL 2 n -1 2 -1 n n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["Fibonacci", "[", "n_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "5"], " ", RowBox[List["(", RowBox[List[RowBox[List["LucasL", "[", RowBox[List["2", " ", "n"]], "]"]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]]]], ")"]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29