A042218 Numerators of continued fraction convergents to sqrt(635).

25, 126, 6325, 31751, 1593875, 8001126, 401650175, 2016252001, 101214250225, 508087503126, 25505589406525, 128036034535751, 6427307316194075, 32264572615506126, 1619655938091500375

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,252,0,-1).

Formula

G.f.: (25 +126*x +25*x^2 -x^3)/(x^4 -252*x^2 +1). - Vincenzo Librandi, Nov 19 2013

a(n) = 252*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 19 2013

Mathematica

Numerator[Convergents[Sqrt[635], 30]] (* Harvey P. Dale, Dec 15 2012 *)
CoefficientList[Series[(25 + 126 x + 25 x^2 - x^3)/(x^4 - 252 x^2 + 1), {x, 0, 30}], x](* Vincenzo Librandi, Nov 19 2013 *)

Prog

(Magma) I:=[25, 126, 6325, 31751]; [n le 4 select I[n] else 252*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

Crossrefs

Cf. A042219.

Sequence in context: A201842 A057902 A042216 * A045166 A365872 A232873

Adjacent sequences: A042215 A042216 A042217 * A042219 A042220 A042221

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved