A041945 Denominators of continued fraction convergents to sqrt(495).

1, 4, 177, 712, 31505, 126732, 5607713, 22557584, 998141409, 4015123220, 177663563089, 714669375576, 31623116088433, 127207133729308, 5628737000177985, 22642155134441248, 1001883562915592897, 4030176406796812836, 178329645461975357681, 717348758254698243560

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,178,0,-1).

Formula

G.f.: -(x^2-4*x-1) / (x^4-178*x^2+1). - Colin Barker, Nov 27 2013

a(n) = 178*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator[Convergents[Sqrt[495], 30]] (* Harvey P. Dale, Aug 22 2013 *)
CoefficientList[Series[(1 + 4 x - x^2)/(x^4 - 178 x^2 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 27 2013 *)
LinearRecurrence[{0, 178, 0, -1}, {1, 4, 177, 712}, 20] (* Harvey P. Dale, Aug 13 2021 *)

Prog

(Magma) I:=[1, 4, 177, 712]; [n le 4 select I[n] else 178*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A041944, A040472.

Sequence in context: A113254 A210780 A127606 * A300387 A082393 A176351

Adjacent sequences: A041942 A041943 A041944 * A041946 A041947 A041948

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved