A042190 Numerators of continued fraction convergents to sqrt(620).

24, 25, 224, 249, 12176, 12425, 111576, 124001, 6063624, 6187625, 55564624, 61752249, 3019672576, 3081424825, 27671071176, 30752496001, 1503790879224, 1534543375225, 13780137881024, 15314681256249

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, 498, 0, 0, 0, -1).

Formula

G.f.: (24 +25*x +224*x^2 +249*x^3 +224*x^4 -25*x^5 +24*x^6 -x^7)/(1 -498*x^4 +x^8). - Vincenzo Librandi, Nov 18 2013

a(n) = 498*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[620], 30]] (* or *) CoefficientList[Series[(24 + 25 x + 224 x^2 + 249 x^3 + 224 x^4 - 25 x^5 + 24 x^6 - x^7)/(1 - 498 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 18 2013 *)
LinearRecurrence[{0, 0, 0, 498, 0, 0, 0, -1}, {24, 25, 224, 249, 12176, 12425, 111576, 124001}, 20] (* Harvey P. Dale, Dec 15 2014 *)

Prog

(Magma) I:=[24, 25, 224, 249, 12176, 12425, 111576, 124001]; [n le 8 select I[n] else 498*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Crossrefs

Cf. A042191.

Sequence in context: A042184 A042186 A042188 * A042192 A042194 A042196

Adjacent sequences: A042187 A042188 A042189 * A042191 A042192 A042193

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved