OFFSET
0,1
COMMENTS
Subset of |A002316| (conjectured).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,52,0,-1).
FORMULA
G.f.: (-x^3+5x^2+26x+5)/(x^4-52x^2+1).
From Gerry Martens, Jul 11 2015: (Start)
Interspersion of 2 sequences [a0(n),a1(n)]:
a0(n) = ((-5-3*sqrt(3))/(26+15*sqrt(3))^n+(-5+3*sqrt(3))*(26+15*sqrt(3))^n)/2.
a1(n) = (1/(26+15*sqrt(3))^n+(26+15*sqrt(3))^n)/2. (End)
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[27], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*)
Numerator/@Convergents[Sqrt[27], 20] (* Harvey P. Dale, Jul 21 2011 *)
CoefficientList[Series[(- x^3 + 5 x^2 + 26 x + 5)/(x^4 - 52 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 28 2013 *)
a0[n_] := (-5-3*Sqrt[3]+(-5+3*Sqrt[3])*(26+15*Sqrt[3])^(2*n))/(2*(26+15*Sqrt[3])^n) // Simplify
a1[n_] := (1+(26+15*Sqrt[3])^(2*n))/(2*(26+15*Sqrt[3])^n) // Simplify
Flatten[MapIndexed[{a0[#], a1[#]}&, Range[10]]] (* Gerry Martens, Jul 10 2015 *)
LinearRecurrence[{0, 52, 0, -1}, {5, 26, 265, 1351}, 30] (* Harvey P. Dale, Dec 12 2015 *)
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved