A041281 Denominators of continued fraction convergents to sqrt(153).

1, 2, 3, 8, 19, 46, 65, 176, 4289, 8754, 13043, 34840, 82723, 200286, 283009, 766304, 18674305, 38114914, 56789219, 151693352, 360175923, 872045198, 1232221121, 3336487440, 81307919681, 165952326802, 247260246483, 660472819768, 1568205886019, 3796884591806

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,4354,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^2-2*x-1)*(x^4+4*x^2+1)*(x^8+22*x^4+1) / ((x^4-8*x^2-1)*(x^4+8*x^2-1)*(x^8+66*x^4+1)). - Colin Barker, Nov 14 2013

a(n) = 4354*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator[Convergents[Sqrt[153], 30]] (* Harvey P. Dale, Mar 04 2013 *)
CoefficientList[Series[-(x^2 - 2 x - 1) (x^4 + 4 x^2 + 1) (x^8 + 22 x^4 + 1)/((x^4 - 8 x^2 - 1) (x^4 + 8 x^2 - 1) (x^8 + 66 x^4 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)

Prog

(Magma) I:=[1, 2, 3, 8, 19, 46, 65, 176, 4289, 8754, 13043, 34840, 82723, 200286, 283009, 766304]; [n le 16 select I[n] else 4354*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A041280, A010204.

Sequence in context: A166302 A347736 A100342 * A078343 A148038 A326301

Adjacent sequences: A041278 A041279 A041280 * A041282 A041283 A041284

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved