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A041228 Numerators of continued fraction convergents to sqrt(126). 2
11, 45, 101, 449, 9979, 40365, 90709, 403201, 8961131, 36247725, 81456581, 362074049, 8047085659, 32550416685, 73147919029, 325142092801, 7226273960651, 29230237935405, 65686749831461, 291977237261249, 6489185969578939, 26248721115577005 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 06:02 EDT 2019. Contains 328046 sequences. (Running on oeis4.)