A042543 Denominators of continued fraction convergents to sqrt(800).

1, 3, 4, 7, 95, 102, 197, 693, 39005, 117708, 156713, 274421, 3724186, 3998607, 7722793, 27166986, 1529074009, 4614389013, 6143463022, 10757852035, 145995539477, 156753391512, 302748930989, 1065000184479, 59942759261813, 180893277969918, 240836037231731

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -3*x^13 +4*x^12 -7*x^11 +95*x^10 -102*x^9 +197*x^8 -693*x^7 -197*x^6 -102*x^5 -95*x^4 -7*x^3 -4*x^2 -3*x -1) / ((x^4 -14*x^2 -1)*(x^4 +14*x^2 -1)*(x^8 +198*x^4 +1)). - Colin Barker, Dec 17 2013

a(n) = 39202*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Jan 23 2014

Mathematica

Denominator[Convergents[Sqrt[800], 30]] (* Harvey P. Dale, May 22 2013 *)

Prog

(Magma) I:=[1, 3, 4, 7, 95, 102, 197, 693, 39005, 117708, 156713, 274421, 3724186, 3998607, 7722793, 27166986]; [n le 16 select I[n] else 39202*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Jan 23 2014

Crossrefs

Cf. A042542, A040771.

Sequence in context: A256725 A041463 A041863 * A041987 A100978 A059077

Adjacent sequences: A042540 A042541 A042542 * A042544 A042545 A042546

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 17 2013

Status

approved