A042750 Numerators of continued fraction convergents to sqrt(906).

30, 301, 18090, 181201, 10890150, 109082701, 6555852210, 65667604801, 3946612140270, 39531789007501, 2375853952590330, 23798071314910801, 1430260132847238390, 14326399399787294701, 861014224120084920450

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,602,0,-1).

Formula

G.f.: (30 +301*x +30*x^2 -x^3)/(1 -602*x^2 +x^4). - Vincenzo Librandi, Dec 03 2013

a(n) = 602*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[906], 30]] (* or *) CoefficientList[Series[(30 + 301 x + 30 x^2 - x^3)/(1 - 602 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)
LinearRecurrence[{0, 602, 0, -1}, {30, 301, 18090, 181201}, 20] (* Harvey P. Dale, Jun 11 2017 *)

Prog

(Magma) I:=[30, 301, 18090, 181201]; [n le 4 select I[n] else 602*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042751.

Sequence in context: A125393 A126551 A328751 * A074994 A134287 A141216

Adjacent sequences: A042747 A042748 A042749 * A042751 A042752 A042753

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved