A041125 Denominators of continued fraction convergents to sqrt(71).

1, 2, 5, 7, 54, 61, 176, 413, 6784, 13981, 34746, 48727, 375835, 424562, 1224959, 2874480, 47216639, 97307758, 241832155, 339139913, 2615811546, 2954951459, 8525714464, 20006380387, 328627800656, 677261981699, 1683151764054, 2360413745753, 18206047984325

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A041124, A010150, A020828, A010523.

Programs

Magma

I:=[1, 2, 5, 7, 54, 61, 176, 413, 6784, 13981, 34746, 48727, 375835, 424562, 1224959, 2874480]; [n le 16 select I[n] else 6960*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[71],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Denominator[Convergents[Sqrt[71], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1},{1,2,5,7,54,61,176,413,6784,13981,34746,48727,375835,424562,1224959,2874480},30] (* Harvey P. Dale, Apr 09 2022 *)

Formula

G.f.: -(x^14 -2*x^13 +5*x^12 -7*x^11 +54*x^10 -61*x^9 +176*x^8 -413*x^7 -176*x^6 -61*x^5 -54*x^4 -7*x^3 -5*x^2 -2*x -1) / (x^16 -6960*x^8 +1). - Colin Barker, Nov 13 2013

a(n) = 6960*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 11 2013

Extensions

More terms from Colin Barker, Nov 13 2013