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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

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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