A042268 Numerators of continued fraction convergents to sqrt(660).

25, 26, 77, 334, 745, 1079, 54695, 55774, 166243, 720746, 1607735, 2328481, 118031785, 120360266, 358752317, 1555369534, 3469491385, 5024860919, 254712537335, 259737398254, 774187333843, 3356486733626

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2158,0,0,0,0,0,-1).

Formula

G.f.: (25 + 26*x + 77*x^2 + 334*x^3 + 745*x^4 + 1079*x^5 + 745*x^6 - 334*x^7 + 77*x^8 - 26*x^9 + 25*x^10 - x^11)/(1 - 2158*x^6 + x^12). - Vincenzo Librandi, Nov 20 2013

a(n) = 2158*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[660], 30]] (* Harvey P. Dale, Oct 11 2011 *)
CoefficientList[Series[(25 + 26 x + 77 x^2 + 334 x^3 + 745 x^4 + 1079 x^5 + 745 x^6 - 334 x^7 + 77 x^8 - 26 x^9 + 25 x^10 - x^11)/(1 - 2158 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)

Prog

(Magma) I:=[25, 26, 77, 334, 745, 1079, 54695, 55774, 166243, 720746, 1607735, 2328481]; [n le 12 select I[n] else 2158*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Crossrefs

Cf. A042269.

Sequence in context: A042272 A042274 A042270 * A042266 A042278 A042276

Adjacent sequences: A042265 A042266 A042267 * A042269 A042270 A042271

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved