A042883 Denominators of continued fraction convergents to sqrt(973).

1, 5, 26, 57, 482, 1021, 5587, 28956, 1800859, 9033251, 46967114, 102967479, 870706946, 1844381371, 10092613801, 52307450376, 3253154537113, 16318080135941, 84843555216818, 186005190569577, 1572885079773434, 3331775350116445, 18231761830355659

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, 1806446, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 - 5*x^13 + 26*x^12 - 57*x^11 + 482*x^10 - 1021*x^9 + 5587*x^8 - 28956*x^7 - 5587*x^6 - 1021*x^5 - 482*x^4 - 57*x^3 - 26*x^2 - 5*x - 1) / (x^16 - 1806446*x^8 + 1). - Colin Barker, Dec 25 2013

a(n) = 1806446*a(n-8) - a(n-16) for n > 15. - Vincenzo Librandi, Jan 31 2014

Mathematica

Denominator[Convergents[Sqrt[973], 40]] (* Harvey P. Dale, May 04 2012 *)

Prog

(Magma) I:=[1, 5, 26, 57, 482, 1021, 5587, 28956, 1800859, 9033251, 46967114, 102967479, 870706946, 1844381371, 10092613801, 52307450376]; [n le 16 select I[n] else 1806446*Self(n-8)-Self(n-16): n in [1..35]]; // Vincenzo Librandi, Jan 31 2014

Crossrefs

Cf. A042882, A040941.

Sequence in context: A273272 A273248 A273301 * A273701 A273709 A139273

Adjacent sequences: A042880 A042881 A042882 * A042884 A042885 A042886

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 25 2013

Status

approved