A041095 Denominators of continued fraction convergents to sqrt(55).

1, 2, 5, 12, 173, 358, 889, 2136, 30793, 63722, 158237, 380196, 5480981, 11342158, 28165297, 67672752, 975583825, 2018840402, 5013264629, 12045369660, 173648439869, 359342249398, 892332938665, 2144008126728, 30908446712857, 63960901552442, 158830249817741

Offset

0,2

Links

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

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

Formula

G.f.: -(x^2-2*x-1)*(x^4+6*x^2+1) / (x^8-178*x^4+1). - Colin Barker, Nov 12 2013

a(n) = 178*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator[Convergents[Sqrt[55], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 178, 0, 0, 0, -1}, {1, 2, 5, 12, 173, 358, 889, 2136}, 30] (* Harvey P. Dale, Nov 24 2022 *)

Prog

(Magma) I:=[1, 2, 5, 12, 173, 358, 889, 2136]; [n le 8 select I[n] else 178*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041094, A010141, A010508, A020812.

Sequence in context: A197706 A205082 A060807 * A041333 A197950 A041715

Adjacent sequences: A041092 A041093 A041094 * A041096 A041097 A041098

Keyword

nonn,cofr,easy,frac

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved