A041866 Numerators of continued fraction convergents to sqrt(455).

21, 64, 2709, 8191, 346731, 1048384, 44378859, 134184961, 5680147221, 17174626624, 727014465429, 2198218022911, 93052171427691, 281354732305984, 11909950928279019, 36011207517143041, 1524380666648286741

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,128,0,-1).

Formula

G.f.: -(x^3-21*x^2-64*x-21)/(x^4-128*x^2+1). - Vincenzo Librandi, Nov 11 2013

a(n) = 128*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 11 2013

Mathematica

Numerator[Convergents[Sqrt[455], 30]] (* or *) CoefficientList[Series[-(x^3 - 21 x^2 - 64 x - 21)/(x^4 - 128 x^2 + 1), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 11 2013 *)

Prog

(Magma) I:=[21, 64, 2709, 8191]; [n le 4 select I[n] else 128*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 11 2013

Crossrefs

Cf. A041867.

Sequence in context: A041862 A041860 A041864 * A020211 A014641 A259677

Adjacent sequences: A041863 A041864 A041865 * A041867 A041868 A041869

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved