A042202 Numerators of continued fraction convergents to sqrt(627).

25, 626, 31325, 783751, 39218875, 981255626, 49102000175, 1228531260001, 61475665000225, 1538120156265626, 76967483478281525, 1925725207113303751, 96363227839143469075, 2411006421185700030626, 120646684287124145000375

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1252,0,-1).

Formula

G.f.: (25 +626*x +25*x^2 -x^3)/(1 -1252*x^2 +x^4). - Vincenzo Librandi, Nov 19 2013

a/n) = 1252*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 19 2013

Mathematica

Numerator[Convergents[Sqrt[627], 20]] (* Harvey P. Dale, Oct 20 2012 *)
CoefficientList[Series[(25 + 626 x + 25 x^2 - x^3)/(x^4 - 1252 x^2 + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 19 2013 *)

Prog

(Magma) I:=[25, 626, 31325, 783751]; [n le 4 select I[n] else 1252*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

Crossrefs

Cf. A042203.

Sequence in context: A207216 A171299 A009969 * A203341 A260048 A152256

Adjacent sequences: A042199 A042200 A042201 * A042203 A042204 A042205

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved