A042397 Denominators of continued fraction convergents to sqrt(725).

1, 1, 13, 27, 337, 364, 19265, 19629, 254813, 529255, 6605873, 7135128, 377632529, 384767657, 4994844413, 10374456483, 129488322209, 139862778692, 7402352814193, 7542215592885, 97908939928813, 203360095450511, 2538230085334945, 2741590180785456

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 19602, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10 -x^9 +13*x^8 -27*x^7 +337*x^6 -364*x^5 -337*x^4 -27*x^3 -13*x^2 -x -1) / ((x^2 -5*x -1)*(x^2 +5*x -1)*(x^4 -5*x^3 +26*x^2 +5*x +1)*(x^4 +5*x^3 +26*x^2 -5*x +1)). - Colin Barker, Dec 10 2013

Mathematica

Denominator[Convergents[Sqrt[725], 30]] (* Harvey P. Dale, May 07 2013 *)
CoefficientList[Series[-(x^10 - x^9 + 13 x^8 - 27 x^7 + 337 x^6 - 364 x^5 - 337 x^4 - 27 x^3 - 13 x^2 - x - 1)/((x^2 - 5 x - 1) (x^2 + 5 x - 1) (x^4 - 5 x^3 + 26 x^2 + 5 x + 1) (x^4 + 5 x^3 + 26 x^2 - 5 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 21 2014 *)

Crossrefs

Cf. A042396, A040698.

Sequence in context: A146380 A146372 A018946 * A041336 A145417 A157206

Adjacent sequences: A042394 A042395 A042396 * A042398 A042399 A042400

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 10 2013

Status

approved