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From Gerry Martens, Jul 11 2015: (Start)
Interspersion of 2 sequences [a0(n),a1(n)] for n>0 :
a1(n) = ((4-sqrt(15))^n+(4+sqrt(15))^n)/2. - _Gerry Martens_, Jul 11 2015(End)
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[15], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
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<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-1).
G.f.: (3+4*x+3*x^2-x^3)/(1-8*x^2+x^4).
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Interspersion of 2 sequences [a0(n),a1(n)] for n>0 :
a0(n) = (-((4-sqrt(15))^n*(3+sqrt(15)))+(-3+sqrt(15))*(4+sqrt(15))^n)/2.
a1(n) = ((4-sqrt(15))^n+(4+sqrt(15))^n)/2. - Gerry Martens, Jul 11 2015
a0[n_] := (-((4-Sqrt[15])^n*(3+Sqrt[15]))+(-3+Sqrt[15])*(4+Sqrt[15])^n)/2 // Simplify
a1[n_] := ((4-Sqrt[15])^n+(4+Sqrt[15])^n)/2 // Simplify
Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *)
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<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-1).
<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (0,8,0,-1).
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[15], n]]], {n, 1, 50}] (*From _Vladimir Joseph Stephan Orlovsky, _, Mar 17 2011*)