A042568 Numerators of continued fraction convergents to sqrt(813).

28, 29, 57, 1055, 1112, 2167, 122464, 124631, 247095, 4572341, 4819436, 9391777, 530758948, 540150725, 1070909673, 19816524839, 20887434512, 40703959351, 2300309158168, 2341013117519, 4641322275687

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4334,0,0,0,0,0,-1).

Formula

G.f.: (28 + 29*x + 57*x^2 + 1055*x^3 + 1112*x^4 + 2167*x^5 + 1112*x^6 - 1055*x^7 + 57*x^8 - 29*x^9 + 28*x^10 - x^11)/(1 - 4334*x^6 + x^12). - Vincenzo Librandi, Nov 28 2013

a(n) = 4334*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 28 2013

Mathematica

Numerator[Convergents[Sqrt[813], 30]] (* Harvey P. Dale, Aug 20 2012 *)
CoefficientList[Series[(28 + 29 x + 57 x^2 + 1055 x^3 + 1112 x^4 + 2167 x^5 + 1112 x^6 - 1055 x^7 + 57 x^8 - 29 x^9 + 28 x^10 - x^11)/(1 - 4334 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 28 2013 *)

Prog

(Magma) I:=[28, 29, 57, 1055, 1112, 2167, 122464, 124631, 247095, 4572341, 4819436, 9391777]; [n le 12 select I[n] else 4334*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 28 2013

Crossrefs

Cf. A042569.

Sequence in context: A042574 A042572 A042570 * A162302 A042592 A042594

Adjacent sequences: A042565 A042566 A042567 * A042569 A042570 A042571

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved