A041109 Denominators of continued fraction convergents to sqrt(62).

1, 1, 7, 8, 119, 127, 881, 1008, 14993, 16001, 110999, 127000, 1888999, 2015999, 13984993, 16000992, 237998881, 253999873, 1761998119, 2015997992, 29985970007, 32001967999, 221997778001, 253999746000, 3777994222001, 4031993968001, 27969958030007

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,126,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+8*x^2+1) / (x^8-126*x^4+1). - Colin Barker, Nov 12 2013

a(n) = 126*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator[Convergents[Sqrt[62], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 126, 0, 0, 0, -1}, {1, 1, 7, 8, 119, 127, 881, 1008}, 30] (* Harvey P. Dale, Oct 26 2016 *)

Prog

(Magma) I:=[1, 1, 7, 8, 119, 127, 881, 1008]; [n le 8 select I[n] else 126*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041108, A010146, A020819, A010515.

Sequence in context: A103680 A219518 A029496 * A041110 A041259 A371104

Adjacent sequences: A041106 A041107 A041108 * A041110 A041111 A041112

Keyword

nonn,cofr,easy,frac

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved