A042416 Numerators of continued fraction convergents to sqrt(736).

27, 190, 217, 624, 841, 2306, 3147, 24335, 1317237, 9244994, 10562231, 30369456, 40931687, 112232830, 153164517, 1184384449, 64109924763, 449953857790, 514063782553, 1478081422896, 1992145205449

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,48670,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^15 -27*x^14 +190*x^13 -217*x^12 +624*x^11 -841*x^10 +2306*x^9 -3147*x^8 -24335*x^7 -3147*x^6 -2306*x^5 -841*x^4 -624*x^3 -217*x^2 -190*x -27)/(x^16 -48670*x^8 +1). - Vincenzo Librandi, Nov 23 2013

a(n) = 48670*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[736], 30]] (* or *) CoefficientList[Series[-(x^15 - 27 x^14 + 190 x^13 - 217 x^12 + 624 x^11 - 841 x^10 + 2306 x^9 - 3147 x^8 - 24335 x^7 - 3147 x^6 - 2306 x^5 - 841 x^4 - 624 x^3 - 217 x^2 - 190 x - 27)/(x^16 - 48670 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)

Prog

(Magma) I:=[27, 190, 217, 624, 841, 2306, 3147, 24335, 1317237, 9244994, 10562231, 30369456, 40931687, 112232830, 153164517, 1184384449]; [n le 16 select I[n] else 48670*Self(n-8)-Self(n-16): n in [1..30]]; //  Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042417.

Sequence in context: A000499 A365890 A365884 * A216108 A216110 A216112

Adjacent sequences: A042413 A042414 A042415 * A042417 A042418 A042419

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved