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A041229 Denominators of continued fraction convergents to sqrt(126). 2
1, 4, 9, 40, 889, 3596, 8081, 35920, 798321, 3229204, 7256729, 32256120, 716891369, 2899821596, 6516534561, 28965959840, 643767651041, 2604036564004, 5851840779049, 26011399680200, 578102633743449, 2338421934653996, 5254946503051441, 23358207946859760 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

FORMULA

G.f.: (1 + 4*x + 9*x^2 + 40*x^3 - 9*x^4 + 4*x^5 - x^6)/(1 - 898*x^4 + x^8). - Vincenzo Librandi, Dec 13 2013

a(n) = 898*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 13 2013

MATHEMATICA

Denominator[Convergents[Sqrt[126], 30]] (* or *) CoefficientList[Series[(1 + 4 x + 9 x^2 + 40 x^3 - 9 x^4 + 4 x^5 - x^6)/(1 - 898 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 13 2013 *)

LinearRecurrence[{0, 0, 0, 898, 0, 0, 0, -1}, {1, 4, 9, 40, 889, 3596, 8081, 35920}, 30] (* Harvey P. Dale, Aug 20 2017 *)

PROG

(MAGMA) I:=[1, 4, 9, 40, 889, 3596, 8081, 35920]; [n le 8 select I[n] else 898*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

CROSSREFS

Cf. A041228.

Sequence in context: A073414 A085110 A013459 * A042887 A053908 A149165

Adjacent sequences:  A041226 A041227 A041228 * A041230 A041231 A041232

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 13 2013

STATUS

approved

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Last modified February 19 13:25 EST 2020. Contains 332044 sequences. (Running on oeis4.)