A041417 Denominators of continued fraction convergents to sqrt(223).

1, 1, 14, 15, 434, 449, 6271, 6720, 194431, 201151, 2809394, 3010545, 87104654, 90115199, 1258602241, 1348717440, 39022690561, 40371408001, 563850994574, 604222402575, 17482078266674, 18086300669249, 252603986966911, 270690287636160, 7831932040779391

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 448, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+15*x^2+1) / (x^8-448*x^4+1). - Colin Barker, Nov 17 2013

a(n) = 448*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[223], 30]] (* Vincenzo Librandi, Dec 17 2013 *)
LinearRecurrence[{0, 0, 0, 448, 0, 0, 0, -1}, {1, 1, 14, 15, 434, 449, 6271, 6720}, 30] (* Harvey P. Dale, Apr 19 2019 *)

Prog

(Magma) I:=[1, 1, 14, 15, 434, 449, 6271, 6720]; [n le 8 select I[n] else 448*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041416, A040208.

Sequence in context: A033050 A225757 A041416 * A041418 A042733 A225758

Adjacent sequences: A041414 A041415 A041416 * A041418 A041419 A041420

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved