A042420 Numerators of continued fraction convergents to sqrt(738).

27, 163, 8829, 53137, 2878227, 17322499, 938293173, 5647081537, 305880696171, 1840931258563, 99716168658573, 600137943210001, 32507165101998627, 195643128555201763, 10597236107082893829

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,326,0,-1).

Formula

G.f.: (27 + 163*x + 27*x^2 - x^3)/(1 - 326*x^2 + x^4). - Vincenzo Librandi, Nov 24 2013

a(n) = 326*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 24 2013

Mathematica

Numerator[Convergents[Sqrt[738], 30]] (* or *) CoefficientList[Series[(27 + 163 x + 27 x^2 - x^3)/(1 - 326 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 24 2013 *)

Prog

(Magma) I:=[27, 163, 8829, 53137]; [n le 4 select I[n] else 326*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 24 2013

Crossrefs

Cf. A042421.

Sequence in context: A033262 A224001 A042418 * A213285 A174617 A055339

Adjacent sequences: A042417 A042418 A042419 * A042421 A042422 A042423

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved