A042080 Numerators of continued fraction convergents to sqrt(564).

23, 24, 71, 95, 4441, 4536, 13513, 18049, 843767, 861816, 2567399, 3429215, 160311289, 163740504, 487792297, 651532801, 30458301143, 31109833944, 92677969031, 123787802975, 5786916905881, 5910704708856

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,190,0,0,0,-1).

Formula

G.f.: -(x^7 - 23*x^6 + 24*x^5 - 71*x^4 - 95*x^3 - 71*x^2 -24*x - 23)/(x^8 - 190*x^4 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 190*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013

Mathematica

Numerator[Convergents[Sqrt[564], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 71 x^4 - 95 x^3 - 71 x^2 - 24 x - 23)/(x^8 - 190 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)
LinearRecurrence[{0, 0, 0, 190, 0, 0, 0, -1}, {23, 24, 71, 95, 4441, 4536, 13513, 18049}, 30] (* Harvey P. Dale, Apr 18 2015 *)

Prog

(Magma) I:=[23, 24, 71, 95, 4441, 4536, 13513, 18049]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042081.

Sequence in context: A042058 A045859 A042078 * A042076 A042074 A214510

Adjacent sequences: A042077 A042078 A042079 * A042081 A042082 A042083

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved