A042456 Numerators of continued fraction convergents to sqrt(756).

27, 55, 2997, 6049, 329643, 665335, 36257733, 73180801, 3988020987, 8049222775, 438646050837, 885341324449, 48247077571083, 97379496466615, 5306739886768293, 10710859270003201, 583693140466941147

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,110,0,-1).

Formula

G.f.: (27 +55*x +27*x^2 -x^3)/(1 -110*x^2 +x^4). - Vincenzo Librandi, Nov 25 2013

a(n) = 110*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 25 2013

Mathematica

Numerator[Convergents[Sqrt[756], 30]] (* Harvey P. Dale, Sep 14 2012 *)
CoefficientList[Series[(27 + 55 x + 27 x^2 - x^3)/(1 - 110 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 25 2013 *)

Prog

(Magma) I:=[27, 55, 2997, 6049]; [n le 4 select I[n] else 110*Self(n-2)-Self(n-4): n in [1..30]]; //  Vincenzo Librandi, Nov 25 2013

Crossrefs

Cf. A042457.

Sequence in context: A042450 A042452 A042454 * A132768 A352266 A053180

Adjacent sequences: A042453 A042454 A042455 * A042457 A042458 A042459

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved