OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (0,34,0,-1).
FORMULA
G.f.: (4+17*x+4*x^2-x^3)/(1-34*x^2+x^4). - Colin Barker, Jan 02 2012
From Gerry Martens, Jul 11 2015: (Start)
Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
a0(n) = ((-4-3*sqrt(2))/(17+12*sqrt(2))^n+(-4+3*sqrt(2))*(17+12*sqrt(2))^n)/2.
a1(n) = (1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/2. (End)
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[18], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
Numerator[Convergents[Sqrt[18], 20]] (* or *) LinearRecurrence[{0, 34, 0, -1}, {4, 17, 140, 577}, 20] (* Harvey P. Dale, Jun 12 2014 *)
a0[n_] := ((-4-3*Sqrt[2])/(17+12*Sqrt[2])^n+(-4+3*Sqrt[2])*(17+12*Sqrt[2])^n)/2 // Simplify
a1[n_] := (1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/2 // Simplify
Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *)
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved