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A041499 Denominators of continued fraction convergents to sqrt(266). 2
1, 3, 13, 42, 1357, 4113, 17809, 57540, 1859089, 5634807, 24398317, 78829758, 2546950573, 7719681477, 33425676481, 107996710920, 3489320425921, 10575957988683, 45793152380653, 147955415130642, 4780366436561197, 14489054724814233, 62736585335818129 (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 (0,0,0,1370,0,0,0,-1).

FORMULA

G.f.: -(x^2-3*x-1)*(x^4+14*x^2+1) / (x^8-1370*x^4+1). - Colin Barker, Nov 18 2013

a(n) = 1370*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 19 2013

MATHEMATICA

Denominator/@Convergents[Sqrt[266], 20]  (* Harvey P. Dale, Apr 11 2011 *)

CoefficientList[Series[(1 + 3 x - x^2) (x^4 + 14 x^2 + 1)/(x^8 - 1370 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)

PROG

(MAGMA) I:=[1, 3, 13, 42, 1357, 4113, 17809, 57540]; [n le 8 select I[n] else 1370*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

CROSSREFS

Cf. A041498, A040249.

Sequence in context: A109224 A106050 A074425 * A093923 A163182 A267455

Adjacent sequences:  A041496 A041497 A041498 * A041500 A041501 A041502

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 18 2013

STATUS

approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)