A041045 Denominators of continued fraction convergents to sqrt(28).

1, 3, 7, 24, 247, 765, 1777, 6096, 62737, 194307, 451351, 1548360, 15934951, 49353213, 114641377, 393277344, 4047414817, 12535521795, 29118458407, 99890897016, 1028027428567, 3183973182717, 7395973794001

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,254,0,0,0,-1).

Formula

a(n) = 254*a(n-4)-a(n-8). G.f.: -(x^2-3*x-1)*(x^4+8*x^2+1)/((x^4-16*x^2+1)*(x^4+16*x^2+1)). [Colin Barker, Jul 16 2012]

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[28], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
CoefficientList[Series[- (x^2 - 3 x - 1) (x^4 + 8 x^2 + 1)/((x^4 - 16 x^2 + 1) (x^4 + 16 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 23 2013 *)

Crossrefs

Cf. A010479, A041044.

Sequence in context: A005642 A019055 A300515 * A041563 A042657 A031875

Adjacent sequences: A041042 A041043 A041044 * A041046 A041047 A041048

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved