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A041687 Denominators of continued fraction convergents to sqrt(363). 2
1, 19, 723, 13756, 523451, 9959325, 378977801, 7210537544, 274379404473, 5220419222531, 198650309860651, 3779576306574900, 143822549959706851, 2736408025541005069, 104127327520517899473, 1981155630915381095056, 75388041302304999511601 (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 (0,724,0,-1).

FORMULA

G.f.: -(x^2-19*x-1) / (x^4-724*x^2+1). - Colin Barker, Nov 21 2013

a(n) = 724*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 22 2013

MATHEMATICA

Denominator[Convergents[Sqrt[363], 20]] (* Harvey P. Dale, Dec 10 2013 *)

CoefficientList[Series[(1 + 19 x - x^2)/(x^4 - 724 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

PROG

(MAGMA) I:=[1, 19, 723, 13756]; [n le 4 select I[n] else 724*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

CROSSREFS

Cf. A041686, A040343.

Sequence in context: A231160 A078986 A180990 * A041684 A157165 A201708

Adjacent sequences:  A041684 A041685 A041686 * A041688 A041689 A041690

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Additional term from Colin Barker, Nov 21 2013

STATUS

approved

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Last modified November 18 07:22 EST 2019. Contains 329252 sequences. (Running on oeis4.)