A042689 Denominators of continued fraction convergents to sqrt(874).

1, 1, 2, 7, 16, 55, 71, 126, 7379, 7505, 14884, 52157, 119198, 409751, 528949, 938700, 54973549, 55912249, 110885798, 388569643, 888025084, 3052644895, 3940669979, 6993314874, 409552932671, 416546247545, 826099180216, 2894843788193, 6615786756602

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, 7450, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +16*x^10 -55*x^9 +71*x^8 -126*x^7 -71*x^6 -55*x^5 -16*x^4 -7*x^3 -2*x^2 -x -1) / (x^16 -7450*x^8 +1). - Colin Barker, Dec 21 2013

a(n) = 7450*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[874], 30]] (* Vincenzo Librandi Dec 21 2013 *)

Prog

(Magma) I:=[1, 1, 2, 7, 16, 55, 71, 126, 7379, 7505, 14884, 52157, 119198, 409751, 528949, 938700]; [n le 16 select I[n] else 7450*Self(n-8)-Self(n-16): n in [1..70]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A042688, A040844.

Sequence in context: A084079 A286848 A239425 * A073998 A129444 A079815

Adjacent sequences: A042686 A042687 A042688 * A042690 A042691 A042692

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 21 2013

Status

approved