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A041499

Denominators of continued fraction convergents to sqrt(266).

1, 3, 13, 42, 1357, 4113, 17809, 57540, 1859089, 5634807, 24398317, 78829758, 2546950573, 7719681477, 33425676481, 107996710920, 3489320425921, 10575957988683, 45793152380653, 147955415130642, 4780366436561197, 14489054724814233, 62736585335818129

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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 (0,0,0,1370,0,0,0,-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