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A041812 Numerators of continued fraction convergents to sqrt(427). 2
20, 21, 41, 62, 2521, 2583, 5104, 7687, 312584, 320271, 632855, 953126, 38757895, 39711021, 78468916, 118179937, 4805666396, 4923846333, 9729512729, 14653359062, 595863875209, 610517234271, 1206381109480 (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, 124, 0, 0, 0, -1).

FORMULA

G.f.: (20+21*x+41*x^2+62*x^3+41*x^4-21*x^5+20*x^6-x^7)/(1-124*x^4+x^8). - Vincenzo Librandi, Nov 09 2013

a(n) = 124*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 09 2013

MATHEMATICA

Numerator[Convergents[Sqrt[427], 30]] (* or *) CoefficientList[Series[(20 + 21 x + 41 x^2 + 62 x^3 + 41 x^4 - 21 x^5 + 20 x^6 - x^7)/(1 - 124 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 09 2013 *)

PROG

(MAGMA) I:=[20, 21, 41, 62, 2521, 2583, 5104, 7687]; [n le 8 select I[n] else 124*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Nov 09 2013

CROSSREFS

Cf. A041813.

Sequence in context: A041808 A041810 A042855 * A041806 A041804 A041802

Adjacent sequences:  A041809 A041810 A041811 * A041813 A041814 A041815

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 24 06:56 EDT 2019. Contains 321444 sequences. (Running on oeis4.)