A041131 Denominators of continued fraction convergents to sqrt(74).

1, 1, 2, 3, 5, 83, 88, 171, 259, 430, 7139, 7569, 14708, 22277, 36985, 614037, 651022, 1265059, 1916081, 3181140, 52814321, 55995461, 108809782, 164805243, 273615025, 4542645643, 4816260668, 9358906311, 14175166979, 23534073290, 390720339619, 414254412909

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,86,0,0,0,0,1).

Formula

G.f.: -(x^4-3*x^3+4*x^2-2*x+1)*(x^4+2*x^3+4*x^2+3*x+1) / (x^10+86*x^5-1). - Colin Barker, Nov 13 2013

a(n) = 86*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator/@Convergents[Sqrt[74], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^4 - 3 x^3 + 4 x^2 - 2 x + 1) (x^4 + 2 x^3 + 4 x^2 + 3 x + 1)/(x^10 + 86 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 0, 86, 0, 0, 0, 0, 1}, {1, 1, 2, 3, 5, 83, 88, 171, 259, 430}, 50] (* Harvey P. Dale, Nov 09 2017 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 83, 88, 171, 259, 430]; [n le 10 select I[n] else 86*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041130, A010152, A020831, A010526.

Sequence in context: A029975 A042787 A270355 * A084960 A087543 A124121

Adjacent sequences: A041128 A041129 A041130 * A041132 A041133 A041134

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved