A041465 Denominators of continued fraction convergents to sqrt(248).

1, 1, 3, 4, 123, 127, 377, 504, 15497, 16001, 47499, 63500, 1952499, 2015999, 5984497, 8000496, 245999377, 253999873, 753999123, 1007998996, 30993969003, 32001967999, 94997905001, 126999873000, 3904994095001, 4031993968001, 11968982031003, 16000975999004

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,126,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-126*x^4+1). - Colin Barker, Nov 18 2013

a(n) = 126*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[248], 30]] (* Vincenzo Librandi, Dec 18 2013 *)
LinearRecurrence[{0, 0, 0, 126, 0, 0, 0, -1}, {1, 1, 3, 4, 123, 127, 377, 504}, 30] (* Harvey P. Dale, Apr 19 2019 *)

Prog

(Magma) I:=[1, 1, 3, 4, 123, 127, 377, 504]; [n le 8 select I[n] else 126*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041464, A040232.

Sequence in context: A041351 A266516 A066496 * A004124 A175504 A308944

Adjacent sequences: A041462 A041463 A041464 * A041466 A041467 A041468

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved