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http://functions.wolfram.com/04.22.03.0003.01
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LucasL[n] == Round[GoldenRatio^n] /; Element[n, Integers] && n > 1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LucasL", "[", "n", "]"]], "\[Equal]", RowBox[List["Round", "[", SuperscriptBox["GoldenRatio", "n"], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "1"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> n </mi> </msub> <mo>  </mo> <mrow> <mo> ⌊ </mo> <msup> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mi> n </mi> </msup> <mo> ⌉ </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> > </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> n </mi> </msub> <mo>  </mo> <mrow> <mo> ⌊ </mo> <msup> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mi> n </mi> </msup> <mo> ⌉ </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> > </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LucasL", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Round", "[", SuperscriptBox["GoldenRatio", "n"], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "1"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
