A041293 Denominators of continued fraction convergents to sqrt(159).

1, 1, 2, 3, 5, 18, 23, 41, 64, 105, 2584, 2689, 5273, 7962, 13235, 47667, 60902, 108569, 169471, 278040, 6842431, 7120471, 13962902, 21083373, 35046275, 126222198, 161268473, 287490671, 448759144, 736249815, 18118754704, 18855004519, 36973759223, 55828763742

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, 0, 0, 0, 0, 0, 2648, 0, 0, 0, 0, 0, 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^10-21*x^5-1) / (x^20-2648*x^10+1). - Colin Barker, Nov 14 2013

a(n) = 2648*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[159], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 18, 23, 41, 64, 105, 2584, 2689, 5273, 7962, 13235, 47667, 60902, 108569, 169471, 278040]; [n le 20 select I[n] else 2648*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041292, A010208.

Sequence in context: A121510 A132346 A284530 * A041713 A042555 A041891

Adjacent sequences: A041290 A041291 A041292 * A041294 A041295 A041296

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved