A042075 Denominators of continued fraction convergents to sqrt(561).

1, 1, 3, 16, 19, 35, 89, 213, 515, 728, 1243, 6943, 15129, 22072, 1030441, 1052513, 3135467, 16729848, 19865315, 36595163, 93055641, 222706445, 538468531, 761174976, 1299643507, 7259392511, 15818428529, 23077821040, 1077398196369, 1100476017409

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, 0, 0, 0, 0, 1045570, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^26 -x^25 +3*x^24 -16*x^23 +19*x^22 -35*x^21 +89*x^20 -213*x^19 +515*x^18 -728*x^17 +1243*x^16 -6943*x^15 +15129*x^14 -22072*x^13 -15129*x^12 -6943*x^11 -1243*x^10 -728*x^9 -515*x^8 -213*x^7 -89*x^6 -35*x^5 -19*x^4 -16*x^3 -3*x^2 -x -1)/(x^28 -1045570*x^14 +1). - Vincenzo Librandi, Jan 14 2014

a(n) = 1045570*a(n-14) - a(n-28)for n>27. - Vincenzo Librandi, Jan 14 2014

Mathematica

Denominator[Convergents[Sqrt[561], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 16 x^23 + 19 x^22 - 35 x^21 + 89 x^20 - 213 x^19 + 515 x^18 - 728 x^17 + 1243 x^16 - 6943 x^15 + 15129 x^14 - 22072 x^13 - 15129 x^12 - 6943 x^11 - 1243 x^10 - 728 x^9 - 515 x^8 - 213 x^7 - 89 x^6 - 35 x^5 - 19 x^4 - 16 x^3 - 3 x^2 - x - 1)/(x^28 - 1045570 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 14 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1045570, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 16, 19, 35, 89, 213, 515, 728, 1243, 6943, 15129, 22072, 1030441, 1052513, 3135467, 16729848, 19865315, 36595163, 93055641, 222706445, 538468531, 761174976, 1299643507, 7259392511, 15818428529, 23077821040}, 30] (* Harvey P. Dale, Mar 01 2015 *)

Crossrefs

Cf. A042074.

Sequence in context: A103655 A022126 A127006 * A342716 A042777 A041461

Adjacent sequences: A042072 A042073 A042074 * A042076 A042077 A042078

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Jan 14 2014

Status

approved