A041944 Numerators of continued fraction convergents to sqrt(495).

22, 89, 3938, 15841, 700942, 2819609, 124763738, 501874561, 22207244422, 89330852249, 3952764743378, 15900389825761, 703569917076862, 2830180058133209, 125231492474938058, 503756149957885441

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,178,0,-1).

Formula

G.f.: (22 + 89*x + 22*x^2 - x^3)/(1 - 178*x^2 + x^4). - Vincenzo Librandi, Nov 12 2013

a(n) = 178*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[495], 30]] (* or *) CoefficientList[Series[(22 + 89 x + 22 x^2 - x^3)/(1 - 178 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)
LinearRecurrence[{0, 178, 0, -1}, {22, 89, 3938, 15841}, 30] (* Harvey P. Dale, Dec 07 2015 *)

Prog

(Magma) I:=[22, 89, 3938, 15841]; [n le 4 select I[n] else 178*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 12 2013

Crossrefs

Cf. A041945.

Sequence in context: A041940 A041942 A231265 * A230357 A145769 A256152

Adjacent sequences: A041941 A041942 A041943 * A041945 A041946 A041947

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved