A041605 Denominators of continued fraction convergents to sqrt(320).

1, 1, 8, 9, 314, 323, 2575, 2898, 101107, 104005, 829142, 933147, 32556140, 33489287, 266981149, 300470436, 10482975973, 10783446409, 85967100836, 96750547245, 3375485707166, 3472236254411, 27681139488043, 31153375742454, 1086895914731479, 1118049290473933

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,322,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+9*x^2+1) / ((x^2-4*x-1)*(x^2+4*x-1)*(x^4+18*x^2+1)). - Colin Barker, Nov 19 2013

a(n) = 322*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[320], 30]] (* Vincenzo Librandi Dec 21 2013 *)

Prog

(Magma) I:=[1, 1, 8, 9, 314, 323, 2575, 2898]; [n le 8 select I[n] else 322*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A041604, A040302.

Sequence in context: A307947 A175849 A294468 * A239524 A115073 A298020

Adjacent sequences: A041602 A041603 A041604 * A041606 A041607 A041608

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved