A041377 Denominators of continued fraction convergents to sqrt(203).

1, 4, 113, 456, 12881, 51980, 1468321, 5925264, 167375713, 675428116, 19079362961, 76992879960, 2174880001841, 8776512887324, 247917240846913, 1000445476274976, 28260390576546241, 114042007782459940, 3221436608485424561, 12999788441724158184

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,114,0,-1).

Formula

G.f.: -(x^2-4*x-1) / (x^4-114*x^2+1). - Colin Barker, Nov 16 2013

a(n) = 114*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[203], 30]] (* Vincenzo Librandi, Dec 16 2013 *)
LinearRecurrence[{0, 114, 0, -1}, {1, 4, 113, 456}, 20] (* Harvey P. Dale, Oct 18 2014 *)

Prog

(Magma) I:=[1, 4, 113, 456]; [n le 4 select I[n] else 114*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041376, A040188.

Sequence in context: A085522 A263416 A078780 * A103499 A298331 A299394

Adjacent sequences: A041374 A041375 A041376 * A041378 A041379 A041380

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved