A041295 Denominators of continued fraction convergents to sqrt(160).

1, 1, 2, 3, 17, 20, 37, 57, 1405, 1462, 2867, 4329, 24512, 28841, 53353, 82194, 2026009, 2108203, 4134212, 6242415, 35346287, 41588702, 76934989, 118523691, 2921503573, 3040027264, 5961530837, 9001558101, 50969321342, 59970879443, 110940200785, 170911080228

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1442,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+19*x^4+1) / ((x^4-6*x^2-1)*(x^4+6*x^2-1)*(x^8+38*x^4+1)). - Colin Barker, Nov 14 2013

a(n) = 1442*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[160], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 17, 20, 37, 57, 1405, 1462, 2867, 4329, 24512, 28841, 53353, 82194]; [n le 16 select I[n] else 1442*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041294, A010209.

Sequence in context: A235628 A140834 A121409 * A128845 A128851 A078737

Adjacent sequences: A041292 A041293 A041294 * A041296 A041297 A041298

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved