A041527 Denominators of continued fraction convergents to sqrt(280).

1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530, 246481, 254011, 754503, 1008514, 2771531, 3780045, 123732971, 127513016, 378759003, 506272019, 1391303041, 1897575060, 62113704961, 64011280021, 190136265003, 254147545024, 698431355051, 952578900075

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,502,0,0,0,0,0,-1).

Formula

a(0)=1, a(1)=1, a(2)=3, a(3)=4, a(4)=11, a(5)=15, a(6)=491, a(7)=506, a(8)=1503, a(9)=2009, a(10)=5521, a(11)=7530, a(n)=502*a(n-6)-a(n-12). - Harvey P. Dale, Aug 13 2012

G.f.: -(x^2-x-1)*(x^8+4*x^6+15*x^4+4*x^2+1) / (x^12-502*x^6+1). - Colin Barker, Nov 18 2013

Mathematica

Denominator[Convergents[Sqrt[280], 30]] (* or *) LinearRecurrence[ {0, 0, 0, 0, 0, 502, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530}, 30] (* Harvey P. Dale, Aug 13 2012 *)
CoefficientList[Series[-(x^2 - x - 1) (x^8 + 4 x^6 + 15 x^4 + 4 x^2 + 1)/(x^12 - 502 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530]; [n le 12 select I[n] else 502*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041526, A040263.

Sequence in context: A046114 A116654 A041020 * A290493 A266384 A248825

Adjacent sequences: A041524 A041525 A041526 * A041528 A041529 A041530

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved