A042014 Numerators of continued fraction convergents to sqrt(531).

23, 530, 24403, 561799, 25867157, 595506410, 27419162017, 631236232801, 29064285870863, 669109811262650, 30808115603952763, 709255768702176199, 32656573475904057917, 751810445714495508290, 34615937076342697439257

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, 1060, 0, -1).

Formula

G.f.: -(x^3-23*x^2-530*x-23)/(x^4-1060*x^2+1). - Vincenzo Librandi, Nov 13 2013

a(n) = 1060*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 13 2013

Mathematica

Numerator[Convergents[Sqrt[531], 30]] (* or *) CoefficientList[Series[-(x^3 - 23 x^2 - 530 x - 23)/(x^4 - 1060 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 13 2013 *)

Prog

(Magma) I:=[23, 530, 24403, 561799]; [n le 4 select I[n] else 1060*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 13 2013

Crossrefs

Cf. A042015.

Sequence in context: A009967 A147642 A057686 * A136670 A062360 A062511

Adjacent sequences: A042011 A042012 A042013 * A042015 A042016 A042017

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved