A041646 Numerators of continued fraction convergents to sqrt(342).

18, 37, 1350, 2737, 99882, 202501, 7389918, 14982337, 546754050, 1108490437, 40452409782, 82013310001, 2992931569818, 6067876449637, 221436483756750, 448940843963137, 16383306866429682, 33215554576822501

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,74,0,-1).

Formula

G.f.: -(x^3-18*x^2-37*x-18)/(x^4-74*x^2+1). - Vincenzo Librandi, Nov 06 2013

a(n) = 74*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 06 2013

Mathematica

Numerator[Convergents[Sqrt[342], 30]] (* or *) CoefficientList[Series[-(x^3 - 18 x^2 - 37 x - 18)/(x^4 - 74 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 06 2013 *)
LinearRecurrence[{0, 74, 0, -1}, {18, 37, 1350, 2737}, 30] (* Harvey P. Dale, Dec 28 2017 *)

Prog

(Magma) I:=[18, 37, 1350, 2737]; [n le 4 select I[n] else 74*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 06 2013

Crossrefs

Cf. A041647.

Sequence in context: A041640 A041642 A041644 * A244412 A114698 A119127

Adjacent sequences: A041643 A041644 A041645 * A041647 A041648 A041649

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved