A041139 Denominators of continued fraction convergents to sqrt(78).

1, 1, 5, 6, 101, 107, 529, 636, 10705, 11341, 56069, 67410, 1134629, 1202039, 5942785, 7144824, 120259969, 127404793, 629879141, 757283934, 12746422085, 13503706019, 66761246161, 80264952180, 1351000481041, 1431265433221, 7076062213925, 8507327647146

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,106,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+6*x^2+1) / (x^8-106*x^4+1). - Colin Barker, Nov 13 2013

a(n) = 106*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator/@Convergents[Sqrt[78], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 6*x^2 + 1)/(x^8 - 106 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 106, 0, 0, 0, -1}, {1, 1, 5, 6, 101, 107, 529, 636}, 30] (* Harvey P. Dale, Sep 15 2018 *)

Prog

(Magma) I:=[1, 1, 5, 6, 101, 107, 529, 636]; [n le 8 select I[n] else 106*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041138, A010156, A020835, A010530.

Sequence in context: A259299 A328561 A053611 * A065354 A078984 A266718

Adjacent sequences: A041136 A041137 A041138 * A041140 A041141 A041142

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved