A041962 Numerators of continued fraction convergents to sqrt(504).

22, 45, 202, 449, 19958, 40365, 181418, 403201, 17922262, 36247725, 162913162, 362074049, 16094171318, 32550416685, 146295838058, 325142092801, 14452547921302, 29230237935405, 131373499662922

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,898,0,0,0,-1).

Formula

G.f.: -(x^7-22*x^6+45*x^5-202*x^4-449*x^3-202*x^2-45*x-22)/(x^8-898*x^4+1). - Vincenzo Librandi, Nov 12 2013

a(n) = 898*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[504], 30]] (* or *) CoefficientList[Series[-(x^7 - 22 x^6 + 45 x^5 - 202 x^4 - 449 x^3 - 202 x^2 - 45 x - 22)/(x^8 - 898 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)

Prog

(Magma) I:=[22, 45, 202, 449, 19958, 40365, 181418, 403201]; [n le 8 select I[n] else 898*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 12 2013

Crossrefs

Cf. A041963.

Sequence in context: A165309 A041960 A041958 * A041964 A041966 A350321

Adjacent sequences: A041959 A041960 A041961 * A041963 A041964 A041965

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved