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

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1).

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

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 *)

Prog

(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

Crossrefs

Cf. A041124, A010150, A020828, A010523.

Sequence in context: A041653 A182785 A358381 * A293592 A042257 A343833

Adjacent sequences: A041122 A041123 A041124 * A041126 A041127 A041128

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 13 2013

Status

approved