A041241 Denominators of continued fraction convergents to sqrt(132).

1, 2, 45, 92, 2069, 4230, 95129, 194488, 4373865, 8942218, 201102661, 411147540, 9246348541, 18903844622, 425130930225, 869165705072, 19546776441809, 39962718588690, 898726585392989, 1837415889374668, 41321876151635685, 84481168192646038

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,46,0,-1).

Formula

G.f.: -(x^2-2*x-1) / (x^4-46*x^2+1). - Colin Barker, Nov 14 2013

a(n) = 46*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 13 2013

a(2*n) = A042011(2*n) = numerator of continued fraction [4,11,4,11,...,4,11] with n pairs of 4,11. - Greg Dresden, Aug 10 2021

Mathematica

Denominator[Convergents[Sqrt[132], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 46, 0, -1}, {1, 2, 45, 92}, 30] (* Harvey P. Dale, Jun 15 2022 *)

Prog

(Magma) I:=[1, 2, 45, 92]; [n le 4 select I[n] else 46*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041240, A040120, A042011.

Sequence in context: A264438 A241762 A343424 * A304015 A279680 A305363

Adjacent sequences: A041238 A041239 A041240 * A041242 A041243 A041244

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved