LucasL[n] == (GoldenRatio^n + (1 - GoldenRatio)^n)/ (GoldenRatio + (1 - GoldenRatio)) /; Element[n, Integers]

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

<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[&quot;L&quot;, LucasL] </annotation> </semantics> <mi> n </mi> </msub> <mo> &#63449; </mo> <mfrac> <mrow> <msup> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> <mi> n </mi> </msup> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> <mo> + </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LucasL </ci> <ci> n </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> GoldenRatio </ci> <ci> n </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> GoldenRatio </ci> </apply> </apply> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> GoldenRatio </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> GoldenRatio </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>

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

2007-05-02