A042098 Numerators of continued fraction convergents to sqrt(573).

23, 24, 359, 383, 17977, 18360, 275017, 293377, 13770359, 14063736, 210662663, 224726399, 10548077017, 10772803416, 161367324841, 172140128257, 8079813224663, 8251953352920, 123607160165543

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, 766, 0, 0, 0, -1).

Formula

G.f.: -(x^7 - 23*x^6 + 24*x^5 - 359*x^4 - 383*x^3 - 359*x^2 - 24*x - 23)/(x^8 - 766*x^4 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 766*a(n-4) - a(n-8). Vincenzo Librandi, Nov 16 2013

Mathematica

Numerator[Convergents[Sqrt[573], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 359 x^4 - 383 x^3 - 359 x^2 - 24 x - 23)/(x^8 - 766 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

Prog

(Magma) I:=[23, 24, 359, 383, 17977, 18360, 275017, 293377]; [n le 8 select I[n] else 766*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042099.

Sequence in context: A042092 A042094 A042096 * A041263 A042100 A042101

Adjacent sequences: A042095 A042096 A042097 * A042099 A042100 A042101

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved