A041285 Denominators of continued fraction convergents to sqrt(155).

1, 2, 9, 20, 489, 998, 4481, 9960, 243521, 497002, 2231529, 4960060, 121272969, 247505998, 1111296961, 2470099920, 60393695041, 123257490002, 553423655049, 1230104800100, 30075938857449, 61381982514998, 275603868917441, 612589720349880, 14977757157314561

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,498,0,0,0,-1).

Formula

G.f.: (1 +2*x +9*x^2 +20*x^3 -9*x^4 +2*x^5 -x^6)/(1 -498*x^4 +x^8). - Vincenzo Librandi, Dec 14 2013

a(n) = 498*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator/@Convergents[Sqrt[155], 40] (* Harvey P. Dale, Jul 18 2011 *)
CoefficientList[Series[(1 + 2 x + 9 x^2 + 20 x^3 - 9  x^4 + 2 x^5 - x^6)/(1 - 498 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)

Prog

(Magma) I:=[1, 2, 9, 20, 489, 998, 4481, 9960]; [n le 8 select I[n] else 498*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A041284.

Sequence in context: A002360 A100516 A337015 * A002888 A041963 A298912

Adjacent sequences: A041282 A041283 A041284 * A041286 A041287 A041288

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 14 2013

Status

approved