A042462 Numerators of continued fraction convergents to sqrt(759).

27, 28, 55, 248, 303, 551, 30057, 30608, 60665, 273268, 333933, 607201, 33122787, 33729988, 66852775, 301141088, 367993863, 669134951, 36501281217, 37170416168, 73671697385, 331857205708, 405528903093

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1102,0,0,0,0,0,-1).

Formula

G.f.: (27 + 28*x + 55*x^2 + 248*x^3 + 303*x^4 + 551*x^5 + 303*x^6 - 248*x^7 + 55*x^8 - 28*x^9 + 27*x^10 - x^11)/(1 - 1102*x^6 + x^12). - Vincenzo Librandi, Nov 25 2013

a(n) = 1102*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 25 2013

Mathematica

Numerator[Convergents[Sqrt[759], 30]] (* Harvey P. Dale, Apr 30 2012 *)
CoefficientList[Series[(27 + 28 x + 55 x^2 + 248 x^3 + 303 x^4 + 551 x^5 + 303 x^6 - 248 x^7 + 55 x^8 - 28 x^9 + 27 x^10 - x^11)/(1 - 1102 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 25 2013 *)

Prog

(Magma) I:=[27, 28, 55, 248, 303, 551, 30057, 30608, 60665, 273268, 333933, 607201]; [n le 12 select I[n] else 1102*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 25 2013

Crossrefs

Cf. A042463.

Sequence in context: A042474 A042466 A042464 * A042460 A042458 A141490

Adjacent sequences: A042459 A042460 A042461 * A042463 A042464 A042465

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved