A041902 Numerators of continued fraction convergents to sqrt(473).

21, 22, 65, 87, 3719, 3806, 11331, 15137, 647085, 662222, 1971529, 2633751, 112589071, 115222822, 343034715, 458257537, 19589851269, 20048108806, 59686068881, 79734177687, 3408521531735, 3488255709422

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