A042088 Numerators of continued fraction convergents to sqrt(568).

23, 24, 119, 143, 6697, 6840, 34057, 40897, 1915319, 1956216, 9740183, 11696399, 547774537, 559470936, 2785658281, 3345129217, 156661602263, 160006731480, 796688528183, 956695259663, 44804670472681

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,286,0,0,0,-1).

Formula

G.f.: -(x^7 - 23*x^6 + 24*x^5 - 119*x^4 - 143*x^3 - 119*x^2 - 24*x - 23)/(x^8 - 286*x^4 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 286*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013

Mathematica

Numerator[Convergents[Sqrt[568], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 119 x^4 - 143 x^3 - 119 x^2 - 24 x - 23)/(x^8 - 286 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

Prog

(Magma) I:=[23, 24, 119, 143, 6697, 6840, 34057, 40897]; [n le 8 select I[n] else 286*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042089.

Sequence in context: A214510 A042084 A042082 * A042086 A042090 A042092

Adjacent sequences: A042085 A042086 A042087 * A042089 A042090 A042091

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved