A041155 - OEIS

A041155

Denominators of continued fraction convergents to sqrt(87).

1, 3, 55, 168, 3079, 9405, 172369, 526512, 9649585, 29475267, 540204391, 1650088440, 30241796311, 92375477373, 1693000389025, 5171376644448, 94777779989089, 289504716611715, 5305862678999959, 16207092753611592, 297033532244008615, 907307689485637437

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,56,0,-1).

FORMULA

G.f.: (1 +3*x -x^2)/(x^4 -56*x^2 +1), - Vincenzo Librandi, Dec 12 2013

a(n) = 56*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 12 2013

MATHEMATICA

Denominator/@Convergents[Sqrt[87], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)

CoefficientList[Series[(1 + 3 x - x^2)/(x^4 - 56 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

PROG

(Magma) I:=[1, 3, 55, 168]; [n le 4 select I[n] else 56*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

CROSSREFS

Cf. A041154.

Sequence in context: A088278 A242199 A268661 * A111483 A119152 A119061

Adjacent sequences: A041152 A041153 A041154 * A041156 A041157 A041158

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved