A041401 Denominators of continued fraction convergents to sqrt(215).

1, 1, 2, 3, 86, 89, 175, 264, 7567, 7831, 15398, 23229, 665810, 689039, 1354849, 2043888, 58583713, 60627601, 119211314, 179838915, 5154700934, 5334539849, 10489240783, 15823780632, 453555098479, 469378879111, 922933977590, 1392312856701, 39907693965218

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, 88, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-88*x^4+1). - Colin Barker, Nov 17 2013

a(n) = 88*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[215], 30]] (* Harvey P. Dale, Oct 11 2012 *)
CoefficientList[Series[(1 + x - x^2) (x^4 + 3 x^2 + 1)/(x^8 - 88 x^4 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 17 2013 *)
LinearRecurrence[{0, 0, 0, 88, 0, 0, 0, -1}, {1, 1, 2, 3, 86, 89, 175, 264}, 30] (* Harvey P. Dale, Dec 25 2019 *)

Prog

(Magma) I:=[1, 1, 2, 3, 86, 89, 175, 264]; [n le 8 select I[n] else 88*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041400, A040200.

Sequence in context: A182343 A242370 A153228 * A103013 A246121 A356798

Adjacent sequences: A041398 A041399 A041400 * A041402 A041403 A041404

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved