OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,52,0,-1).
FORMULA
a(n) = 52*a(n-2)-a(n-4). G.f.: -(x^2-5*x-1)/(x^4-52*x^2+1). - Colin Barker, Jul 15 2012
From Gerry Martens, Jul 11 2015: (Start)
Interspersion of 2 sequences [a0(n),a1(n)]:
a0(n) = ((9+5*sqrt(3))/(26+15*sqrt(3))^n+(9-5*sqrt(3))*(26+15*sqrt(3))^n)/18.
a1(n) = (-1/(26+15*sqrt(3))^n+(26+15*sqrt(3))^n)/(6*sqrt(3)). (End)
MATHEMATICA
Denominator[Convergents[Sqrt[27], 50]] (* Harvey P. Dale, Apr 22 2012 *)
CoefficientList[Series[- (x^2 - 5 x - 1)/(x^4 - 52 x^2 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 22 2013 *)
a0[n_] := (9+5*Sqrt[3]+(9-5*Sqrt[3])*(26+15*Sqrt[3])^(2*n))/(18*(26+15*Sqrt[3])^n) // Simplify
a1[n_] := (-1+(26+15*Sqrt[3])^(2*n))/(6*Sqrt[3]*(26+15*Sqrt[3])^n) // FullSimplify
Flatten[MapIndexed[{a0[#], a1[#]}&, Range[10]]] (* Gerry Martens, Jul 10 2015 *)
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved