A042540 Numerators of continued fraction convergents to sqrt(799).

28, 85, 113, 424, 23857, 71995, 95852, 359551, 20230708, 61051675, 81282383, 304898824, 17155616527, 51771748405, 68927364932, 258553843201, 14547942584188, 43902381595765, 58450324179953

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, 0, 0, 848, 0, 0, 0, -1).

Formula

G.f.: (28 +85*x +113*x^2 +424*x^3 +113*x^4 -85*x^5 +28 *x^6 -x^7)/(1 -848*x^4 +x^8). - Vincenzo Librandi, Nov 27 2013

a(n) = 848*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 27 2013

Mathematica

Numerator[Convergents[Sqrt[799], 30]] (* or *) CoefficientList[Series[(28 +85 x + 113 x^2 + 424 x^3 + 113 x^4 - 85 x^5 + 28 x^6 - x^7)/(1 - 848 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 27 2013 *)

Prog

(Magma) I:=[28, 85, 113, 424, 23857, 71995, 95852, 359551]; [n le 8 select I[n] else 848*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 27 2013

Crossrefs

Cf. A042541.

Sequence in context: A271735 A280885 A042542 * A042544 A042546 A164689

Adjacent sequences: A042537 A042538 A042539 * A042541 A042542 A042543

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved