A042092 Numerators of continued fraction convergents to sqrt(570).

23, 24, 167, 191, 8953, 9144, 63817, 72961, 3420023, 3492984, 24377927, 27870911, 1306439833, 1334310744, 9312304297, 10646615041, 499056596183, 509703211224, 3557275863527, 4066979074751

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,382,0,0,0,-1).

Formula

G.f.: -(x^7 - 23*x^6 + 24*x^5 - 167*x^4 - 191*x^3 - 167*x^2 - 24*x - 23)/(x^8 - 382*x^4 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 382*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013

Mathematica

Numerator[Convergents[Sqrt[570], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 167 x^4 - 191 x^3 - 167 x^2 - 24 x - 23)/(x^8 - 382 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

Prog

(Magma) I:=[23, 24, 167, 191, 8953, 9144, 63817, 72961]; [n le 8 select I[n] else 382*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042093.

Sequence in context: A042088 A042086 A042090 * A042094 A042096 A042098

Adjacent sequences: A042089 A042090 A042091 * A042093 A042094 A042095

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved