A042598 Numerators of continued fraction convergents to sqrt(828).

28, 29, 115, 259, 892, 1151, 65348, 66499, 264845, 596189, 2053412, 2649601, 150431068, 153080669, 609673075, 1372426819, 4726953532, 6099380351, 346292253188, 352391633539, 1403467153805, 3159325941149

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, 0, 0, 2302, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (28 +29*x +115*x^2 +259*x^3 +892*x^4 +1151*x^5 +892*x^6 -259*x^7 +115*x^8 -29*x^9 +28*x^10 -x^11)/(1 -2302*x^6 +x^12). - Vincenzo Librandi, Nov 29 2013

a(n) = 2302*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 29 2013

Mathematica

Numerator[Convergents[Sqrt[828], 30]] (* or *) CoefficientList[Series[(28 + 29 x + 115 x^2 + 259 x^3 + 892 x^4 + 1151 x^5 + 892 x^6 - 259 x^7 + 115 x^8 - 29 x^9 + 28 x^10 - x^11)/(1 - 2302 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 29 2013 *)

Prog

(Magma) I:=[28, 29, 115, 259, 892, 1151, 65348, 66499, 264845, 596189, 2053412, 2649601]; [n le 12 select I[n] else 2302*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 29 2013

Crossrefs

Cf. A042599.

Sequence in context: A042588 A042586 A042600 * A042596 A042604 A042602

Adjacent sequences: A042595 A042596 A042597 * A042599 A042600 A042601

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved