A041183 Denominators of continued fraction convergents to sqrt(102).

1, 10, 201, 2020, 40601, 408030, 8201201, 82420040, 1656602001, 16648440050, 334625403001, 3362902470060, 67592674804201, 679289650512070, 13653385685045601, 137213146500968080, 2757916315704407201, 27716376303545040090, 557085442386605209001

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,202,0,-1).

Formula

G.f.: (1 +10*x -x^2)/(1 -202*x^2 +x^4). - Vincenzo Librandi, Dec 12 2013

a(n) = 202*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator[Convergents[Sqrt[102], 40]] (* Harvey P. Dale, Sep 29 2011 *)
CoefficientList[Series[(1 + 10 x - x^2)/(1 - 202 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

Prog

(Magma) I:=[1, 10, 201, 2020]; [n le 4 select I[n] else 202*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 12 2013

Crossrefs

Cf. A041182.

Sequence in context: A362723 A178020 A279833 * A210168 A041180 A367200

Adjacent sequences: A041180 A041181 A041182 * A041184 A041185 A041186

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 12 2013

Status

approved