A042314 Numerators of continued fraction convergents to sqrt(684).

26, 157, 183, 340, 4263, 4603, 8866, 57799, 3014414, 18144283, 21158697, 39302980, 492794457, 532097437, 1024891894, 6681448801, 348460229546, 2097442826077, 2445903055623, 4543345881700, 56966053636023

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,115598,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^15 -26*x^14 +157*x^13 -183*x^12 +340*x^11 -4263*x^10 +4603*x^9 -8866*x^8 -57799*x^7 -8866*x^6 -4603*x^5 -4263*x^4 -340*x^3 -183*x^2 -157*x -26)/(x^16 -115598*x^8 +1). - Vincenzo Librandi Nov 21 2013

a(n) = 115598*a(n-8) - a(n-16), - Vincenzo Librandi, Nov 21 2013

Mathematica

Numerator[Convergents[Sqrt[684], 30]] (* or *) CoefficientList[Series[-(x^15 - 26 x^14 + 157 x^13 - 183 x^12 + 340 x^11 - 4263 x^10 + 4603 x^9 - 8866 x^8 - 57799 x^7 - 8866 x^6 - 4603 x^5 - 4263 x^4 - 340 x^3 - 183 x^2 - 157 x - 26)/(x^16 - 115598 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

Prog

(Magma) I:=[26, 157, 183, 340, 4263, 4603, 8866, 57799, 3014414, 18144283, 21158697, 39302980, 492794457, 532097437, 1024891894, 6681448801]; [n le 16 select I[n] else 115598*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

Crossrefs

Cf. A042315.

Sequence in context: A192289 A230906 A232585 * A280213 A200874 A027280

Adjacent sequences: A042311 A042312 A042313 * A042315 A042316 A042317

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved