A042738 Numerators of continued fraction convergents to sqrt(899).

29, 30, 1769, 1799, 106111, 107910, 6364891, 6472801, 381787349, 388260150, 22900876049, 23289136199, 1373670775591, 1396959911790, 82397345659411, 83794305571201, 4942467068789069, 5026261374360270, 296465626781684729, 301491888156044999, 17782995139832294671

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,60,0,-1).

Formula

G.f.: (29 +30*x +29*x^2 -x^3)/(1 -60*x^2 +x^4). - Vincenzo Librandi, Dec 03 2013

a(n) = 60*a(n-2) - a(n-4), - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[899], 30]] (* Harvey P. Dale, Oct 16 2013 *)
CoefficientList[Series[(29 + 30 x + 29 x^2 - x^3)/(1 - 60 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)

Prog

(Magma) I:=[29, 30, 1769, 1799]; [n le 4 select I[n] else 60*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042739.

Sequence in context: A041419 A042736 A042737 * A157498 A031062 A054056

Adjacent sequences: A042735 A042736 A042737 * A042739 A042740 A042741

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 03 2013

Status

approved