A042298 Numerators of continued fraction convergents to sqrt(675).

25, 26, 1325, 1351, 68875, 70226, 3580175, 3650401, 186100225, 189750626, 9673631525, 9863382151, 502842739075, 512706121226, 26138148800375, 26650854921601, 1358680894880425, 1385331749802026, 70625268384981725, 72010600134783751, 3671155275124169275

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,52,0,-1).

Formula

G.f.: -(x^3-25*x^2-26*x-25) / (x^4-52*x^2+1). - Vincenzo Librandi, Nov 21 2013, simplified by Colin Barker, Dec 28 2013

a(n) = 52*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 21 2013, simplified by Colin Barker, Dec 28 2013

Mathematica

Numerator[Convergents[Sqrt[675], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 1325 x^2 + 1351 x^3 + 1325 x^4 - 26 x^5 + 25 x^6 - x^7)/(1 - 2702 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

Prog

(Magma) I:=[25, 26, 1325, 1351, 68875, 70226, 3580175, 3650401]; [n le 8 select I[n] else 2702*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

Crossrefs

Cf. A042299, A040649.

Sequence in context: A041311 A042296 A042297 * A157091 A070662 A350181

Adjacent sequences: A042295 A042296 A042297 * A042299 A042300 A042301

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 28 2013

Status

approved