A042302 Numerators of continued fraction convergents to sqrt(678).

26, 677, 35230, 916657, 47701394, 1241152901, 64587652246, 1680520111297, 87451633439690, 2275422989543237, 118409447089688014, 3080921047321431601, 160326303907804131266, 4171564822650228844517, 217081697081719704046150

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1354,0,-1).

Formula

G.f.: (26 +677*x +26*x^2 -x^3)/(1 -1354*x^2 +x^4). - Vincenzo Librandi, Nov 21 2013

a(n) = 1354*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 21 2013

Mathematica

Numerator[Convergents[Sqrt[678], 20]] (* Harvey P. Dale, Oct 08 2012 *)
CoefficientList[Series[(26 + 677 x + 26 x^2 - x^3)/(1 - 1354 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

Prog

(Magma) I:=[26, 677, 35230, 916657]; [n le 4 select I[n] else 1354*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

Crossrefs

Cf. A042303.

Sequence in context: A188696 A009970 A041313 * A097835 A158643 A181227

Adjacent sequences: A042299 A042300 A042301 * A042303 A042304 A042305

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved