A041762 Numerators of continued fraction convergents to sqrt(402).

20, 401, 16060, 321601, 12880100, 257923601, 10329824140, 206854406401, 8284506080180, 165896976010001, 6644163546480220, 133049167905614401, 5328610879771056260, 106705266763326739601, 4273539281412840640300, 85577490895020139545601

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,802,0,-1).

Formula

G.f.: -(x^3-20*x^2-401*x-20) / (x^4-802*x^2+1). - Vincenzo Librandi, Nov 08 2013, simplified by Colin Barker, Dec 28 2013

a(n) = 802*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 08 2013, simplified by Colin Barker, Dec 28 2013

Mathematica

Numerator[Convergents[Sqrt[402], 30]] (* Harvey P. Dale, Apr 29 2013 *)
CoefficientList[Series[(20 + 401 x + 16060 x^2 + 321601 x^3 + 16060 x^4 - 401 x^5 + 20 x^6 - x^7)/(1 - 643202 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 08 2013 *)

Prog

(Magma) I:=[20, 401, 16060, 321601, 12880100, 257923601, 10329824140, 206854406401]; [n le 8 select I[n] else 643202*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 08 2013

Crossrefs

Cf. A041763, A040381.

Sequence in context: A055476 A223180 A041181 * A196740 A196898 A355966

Adjacent sequences: A041759 A041760 A041761 * A041763 A041764 A041765

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Dec 28 2013

Status

approved