A042402 Numerators of continued fraction convergents to sqrt(728).

26, 27, 1430, 1457, 77194, 78651, 4167046, 4245697, 224943290, 229188987, 12142770614, 12371959601, 655484669866, 667856629467, 35384029402150, 36051886031617, 1910082103046234, 1946133989077851

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, 54, 0, -1).

Formula

G.f.: (26 +27*x +26*x^2 -x^3)/(1 -54*x^2 +x^4). - Vincenzo Librandi, Nov 23 2013

a(n) = 54*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[728], 30]] (* Harvey P. Dale, Feb 24 2013 *)
CoefficientList[Series[(26 + 27 x + 26 x^2 - x^3)/(1 - 54 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)

Prog

(Magma) I:=[26, 27, 1430, 1457]; [n le 4 select I[n] else 54*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042403.

Sequence in context: A042398 A042400 A042401 * A247394 A056081 A081644

Adjacent sequences: A042399 A042400 A042401 * A042403 A042404 A042405

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved