A041681 Denominators of continued fraction convergents to sqrt(359).

1, 1, 18, 19, 702, 721, 12959, 13680, 505439, 519119, 9330462, 9849581, 363915378, 373764959, 6717919681, 7091684640, 262018566721, 269110251361, 4836892839858, 5106003091219, 188653004123742, 193759007214961, 3482556126778079, 3676315133993040

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, 720, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+19*x^2+1) / (x^8-720*x^4+1). - Colin Barker, Nov 21 2013

a(n) = 720*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[359], 30]] (* Harvey P. Dale, Oct 08 2011 *)
CoefficientList[Series[-(x^2 - x-1) (x^4 + 19 x^2 + 1)/(x^8 - 720 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 1, 18, 19, 702, 721, 12959, 13680]; [n le 8 select I[n] else 720*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041680, A040340.

Sequence in context: A197352 A056083 A041680 * A041682 A265946 A027888

Adjacent sequences: A041678 A041679 A041680 * A041682 A041683 A041684

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 21 2013

Status

approved