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A041902 Numerators of continued fraction convergents to sqrt(473). 2
21, 22, 65, 87, 3719, 3806, 11331, 15137, 647085, 662222, 1971529, 2633751, 112589071, 115222822, 343034715, 458257537, 19589851269, 20048108806, 59686068881, 79734177687, 3408521531735, 3488255709422 (list; graph; refs; listen; history; text; internal format)
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, 0, 0, 174, 0, 0, 0, -1).

FORMULA

G.f.: -(x^7-21*x^6+22*x^5-65*x^4-87*x^3-65*x^2-22*x-21)/(x^8-174*x^4+1). - Vincenzo Librandi, Nov 11 2013

a(n) = 174*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 11 2013

MATHEMATICA

Numerator[Convergents[Sqrt[473], 30]] (* or *) CoefficientList[Series[-(x^7 - 21 x^6 + 22 x^5 - 65 x^4 - 87 x^3 - 65 x^2 - 22 x - 21)/(x^8 - 174 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 11 2013 *)

PROG

(MAGMA) I:=[21, 22, 65, 87, 3719, 3806, 11331, 15137]; [n le 8 select I[n] else 174*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 11 2013

CROSSREFS

Cf. A041903.

Sequence in context: A301661 A281364 A041900 * A041898 A041896 A041906

Adjacent sequences:  A041899 A041900 A041901 * A041903 A041904 A041905

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)