A042392 Numerators of continued fraction convergents to sqrt(723).

26, 27, 215, 242, 12799, 13041, 104086, 117127, 6194690, 6311817, 50377409, 56689226, 2998217161, 3054906387, 24382561870, 27437468257, 1451130911234, 1478568379491, 11801109567671, 13279677947162

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, 0, 0, 484, 0, 0, 0, -1).

Formula

G.f.: (26 +27*x +215*x^2 +242*x^3 +215*x^4 -27*x^5 +26 *x^6 -x^7)/(1 -484*x^4 +x^8). - Vincenzo Librandi, Nov 23 2013

a(n) = 484*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[723], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 215 x^2 + 242 x^3 + 215 x^4 - 27 x^5 + 26 x^6 - x^7)/(1 - 484 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)

Prog

(Magma) I:=[26, 27, 215, 242, 12799, 13041, 104086, 117127]; [n le 8 select I[n] else 484*Self(n-4)-Self(n-8): n in [1..30]]; //  Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042393.

Sequence in context: A042384 A042388 A042390 * A136923 A042394 A137118

Adjacent sequences: A042389 A042390 A042391 * A042393 A042394 A042395

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved