A041812 Numerators of continued fraction convergents to sqrt(427).

20, 21, 41, 62, 2521, 2583, 5104, 7687, 312584, 320271, 632855, 953126, 38757895, 39711021, 78468916, 118179937, 4805666396, 4923846333, 9729512729, 14653359062, 595863875209, 610517234271, 1206381109480

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