A041922 Numerators of continued fraction convergents to sqrt(483).

21, 22, 945, 967, 41559, 42526, 1827651, 1870177, 80375085, 82245262, 3534676089, 3616921351, 155445372831, 159062294182, 6836061728475, 6995124022657, 300631270680069, 307626394702726, 13220939848194561

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,44,0,-1).

Formula

G.f.: -(x^3-21*x^2-22*x-21)/(x^4-44*x^2+1). - Vincenzo Librandi, Nov 12 2013

a(n) = 44*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[483], 30]] (* or *) CoefficientList[Series[-(x^3 - 21 x^2 - 22 x - 21)/(x^4 - 44 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)
LinearRecurrence[{0, 44, 0, -1}, {21, 22, 945, 967}, 20] (* Harvey P. Dale, Sep 28 2023 *)

Prog

(Magma) I:=[21, 22, 945, 967]; [n le 4 select I[n] else 44*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 12 2013

Crossrefs

Cf. A041923.

Sequence in context: A041219 A041920 A041921 * A104669 A156891 A095459

Adjacent sequences: A041919 A041920 A041921 * A041923 A041924 A041925

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved