A041835 Denominators of continued fraction convergents to sqrt(438).

1, 1, 13, 14, 573, 587, 7617, 8204, 335777, 343981, 4463549, 4807530, 196764749, 201572279, 2615632097, 2817204376, 115303807137, 118121011513, 1532755945293, 1650876956806, 67567834217533, 69218711174339, 898192368309601, 967411079483940

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 586, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+14*x^2+1) / (x^8-586*x^4+1). - Colin Barker, Nov 25 2013

a(n) = 586*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 25 2013

Mathematica

Denominator[Convergents[Sqrt[438], 30]] (* Vincenzo Librandi, Dec 25 2013 *)
LinearRecurrence[{0, 0, 0, 586, 0, 0, 0, -1}, {1, 1, 13, 14, 573, 587, 7617, 8204}, 30] (* Harvey P. Dale, Oct 25 2015 *)

Prog

(Magma) I:=[1, 1, 13, 14, 573, 587, 7617, 8204]; [n le 8 select I[n] else 586*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 25 2013

Crossrefs

Cf. A041834, A040417.

Sequence in context: A041360 A041361 A041362 * A042505 A156371 A229957

Adjacent sequences: A041832 A041833 A041834 * A041836 A041837 A041838

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 25 2013

Status

approved