A042381 Denominators of continued fraction convergents to sqrt(717).

1, 1, 4, 9, 112, 121, 2048, 2169, 28076, 58321, 203039, 261360, 13793759, 14055119, 55959116, 125973351, 1567639328, 1693612679, 28665442192, 30359054871, 392974100644, 816307256159, 2841895869121, 3658203125280, 193068458383681, 196726661508961

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, 0, 0, 0, 0, 0, 0, 13996798, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^22 -x^21 +4*x^20 -9*x^19 +112*x^18 -121*x^17 +2048*x^16 -2169*x^15 +28076*x^14 -58321*x^13 +203039* x^12 -261360*x^11 -203039*x^10 -58321*x^9 -28076*x^8 -2169*x^7 -2048*x^6 -121*x^5 -112*x^4 -9*x^3 -4*x^2 -x -1)/(x^24 -13996798*x^12 +1). - Vincenzo Librandi, Jan 21 2014

a(n) = 13996798*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Jan 21 2014

Mathematica

Denominator[Convergents[Sqrt[717], 30]] (* Harvey P. Dale, Feb 12 2013 *)
CoefficientList[Series[-(x^22 - x^21 + 4 x^20 - 9 x^19 + 112 x^18 - 121 x^17 + 2048 x^16 -2169 x^15 + 28076 x^14 - 58321 x^13 + 203039 x^12 - 261360 x^11 - 203039 x^10 - 58321 x^9 - 28076 x^8 - 2169 x^7 - 2048 x^6 - 121 x^5 - 112 x^4 - 9 x^3 - 4 x^2 - x - 1)/(x^24 - 13996798 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 21 2014 *)

Prog

(Magma) I:=[1, 1, 4, 9, 112, 121, 2048, 2169, 28076, 58321, 203039, 261360, 13793759, 14055119, 55959116, 125973351, 1567639328, 1693612679, 28665442192, 30359054871, 392974100644, 816307256159, 2841895869121, 3658203125280]; [n le 24 select I[n] else 13996798*Self(n-12)-Self(n-24): n in [1..30]]; // Vincenzo Librandi, Jan 21 2014

Crossrefs

Cf. A042380.

Sequence in context: A117680 A042649 A324024 * A230743 A367075 A033294

Adjacent sequences: A042378 A042379 A042380 * A042382 A042383 A042384

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Jan 21 2014

Status

approved