A041423 Denominators of continued fraction convergents to sqrt(227).

1, 15, 451, 6780, 203851, 3064545, 92140201, 1385167560, 41647167001, 626092672575, 18824427344251, 282992502836340, 8508599512434451, 127911985189353105, 3845868155193027601, 57815934313084767120, 1738323897547736041201

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,452,0,-1).

Formula

G.f.: -(x^2-15*x-1) / (x^4-452*x^2+1). - Colin Barker, Nov 17 2013

a(n) = 452*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[227], 20]] (* Harvey P. Dale, Jul 13 2013 *)
CoefficientList[Series[(1 + 15 x - x^2)/(x^4 - 452 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 17 2013 *)

Prog

(Magma) I:=[1, 15, 451, 6780]; [n le 4 select I[n] else 452*Self(n-2)-Self(n-4): n in [1..100]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041422, A040211.

Sequence in context: A267643 A267666 A020285 * A041420 A036506 A369828

Adjacent sequences: A041420 A041421 A041422 * A041424 A041425 A041426

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved