A041133 Denominators of continued fraction convergents to sqrt(75).

1, 1, 2, 3, 50, 53, 103, 156, 2599, 2755, 5354, 8109, 135098, 143207, 278305, 421512, 7022497, 7444009, 14466506, 21910515, 365034746, 386945261, 751980007, 1138925268, 18974784295, 20113709563, 39088493858, 59202203421, 986323748594, 1045525952015

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,52,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-52*x^4+1). - Colin Barker, Nov 13 2013

a(n) = 52*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator/@Convergents[Sqrt[75], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 3 x^2 + 1)/(x^8 - 52 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 52, 0, 0, 0, -1}, {1, 1, 2, 3, 50, 53, 103, 156}, 40] (* Harvey P. Dale, Aug 03 2024 *)

Prog

(Magma) I:=[1, 1, 2, 3, 50, 53, 103, 156]; [n le 8 select I[n] else 52*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041132, A020832, A010153.

Sequence in context: A191594 A208204 A067092 * A113700 A065646 A268251

Adjacent sequences: A041130 A041131 A041132 * A041134 A041135 A041136

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved