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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• frac

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).

Crossrefs

Cf. A041094, A010141, A010508, A020812.

Programs

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

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 *)

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

Extensions

More terms from Colin Barker, Nov 12 2013