A041228 Numerators of continued fraction convergents to sqrt(126).

11, 45, 101, 449, 9979, 40365, 90709, 403201, 8961131, 36247725, 81456581, 362074049, 8047085659, 32550416685, 73147919029, 325142092801, 7226273960651, 29230237935405, 65686749831461, 291977237261249, 6489185969578939, 26248721115577005

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..150

Index entries for linear recurrences with constant coefficients, signature (0,0,0,898,0,0,0,-1).

Formula

G.f.: (11 +45*x +101*x^2 +449*x^3 +101*x^4 -45*x^5 +11*x^6 -x^7) / ((1 -30*x^2 +x^4)*(1 +30*x^2 +x^4)). [Bruno Berselli, Oct 31 2013]

Mathematica

Numerator[Convergents[Sqrt[126], 30]] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 0, 0, 898, 0, 0, 0, -1}, {11, 45, 101, 449, 9979, 40365, 90709, 403201}, 30] (* Bruno Berselli, Oct 31 2013 *)

Prog

(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((11+45*x+101*x^2+449*x^3+101*x^4-45*x^5+11*x^6-x^7)/((1-30*x^2+x^4)*(1+30*x^2+x^4)))); // Bruno Berselli, Oct 31 2013

Crossrefs

Cf. A041229.

Sequence in context: A068596 A002089 A042521 * A022280 A154106 A232613

Adjacent sequences: A041225 A041226 A041227 * A041229 A041230 A041231

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved