A042306 Numerators of continued fraction convergents to sqrt(680).

26, 339, 17654, 229841, 11969386, 155831859, 8115226054, 105653770561, 5502111295226, 71633100608499, 3730423342937174, 48567136558791761, 2529221524400108746, 32928446953760205459, 1714808463119930792614

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,678,0,-1).

Formula

G.f.: (26 +339*x +26*x^2 -x^3)/(1 -678*x^2 +x^4). - Vincenzo Librandi Nov 21 2013

a(n) = 678*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 21 2013

Mathematica

Numerator[Convergents[Sqrt[680], 30]] (* or *) CoefficientList[Series[(26 + 339 x + 26 x^2 - x^3)/(1 - 678 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

Prog

(Magma) I:=[26, 339, 17654, 229841]; [n le 4 select I[n] else 678*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

Crossrefs

Cf. A042307.

Sequence in context: A126919 A035708 A252826 * A329300 A053494 A054938

Adjacent sequences: A042303 A042304 A042305 * A042307 A042308 A042309

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved