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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy
• less

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).

Crossrefs

Cf. A041923.

Programs

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

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 *)

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