A041951 Denominators of continued fraction convergents to sqrt(498).

1, 3, 19, 421, 2545, 8056, 357009, 1079083, 6831507, 151372237, 915064929, 2896567024, 128364013985, 387988608979, 2456295667859, 54426493301877, 329015255479121, 1041472259739240, 46153794684005681, 139502856311756283, 883170932554543379

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,359554,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -3*x^9 +19*x^8 -421*x^7 +2545*x^6 -8056*x^5 -2545*x^4 -421*x^3 -19*x^2 -3*x -1) / (x^12 -359554*x^6 +1). - Colin Barker, Nov 27 2013

a(n) = 359554*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator[Convergents[Sqrt[498], 30]] (* Vincenzo Librandi, Dec 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 359554, 0, 0, 0, 0, 0, -1}, {1, 3, 19, 421, 2545, 8056, 357009, 1079083, 6831507, 151372237, 915064929, 2896567024}, 30] (* Harvey P. Dale, Oct 21 2016 *)

Prog

(Magma) I:=[1, 3, 19, 421, 2545, 8056, 357009, 1079083, 6831507, 151372237, 915064929, 2896567024]; [n le 12 select I[n] else 359554*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A041950, A040475.

Sequence in context: A195642 A195643 A195638 * A365362 A143762 A228149

Adjacent sequences: A041948 A041949 A041950 * A041952 A041953 A041954

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved