A042121 Denominators of continued fraction convergents to sqrt(585).

1, 5, 11, 16, 75, 91, 257, 1376, 66305, 332901, 732107, 1065008, 4992139, 6057147, 17106433, 91589312, 4413393409, 22158556357, 48730506123, 70889062480, 332286756043, 403175818523, 1138638393089, 6096367783968, 293764292023553, 1474917827901733

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,66562,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -5*x^13 +11*x^12 -16*x^11 +75*x^10 -91*x^9 +257*x^8 -1376*x^7 -257*x^6 -91*x^5 -75*x^4 -16*x^3 -11*x^2 -5*x -1) / ((x^4 -16*x^2 -1)*(x^4 +16*x^2 -1)*(x^8 +258*x^4 +1)). - Colin Barker, Dec 02 2013

a(n) = 66562*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[585], 30]] (* Vincenzo Librandi, Jan 15 2014 *)

Crossrefs

Cf. A042120, A040560.

Sequence in context: A041117 A041491 A058025 * A123082 A084037 A077130

Adjacent sequences: A042118 A042119 A042120 * A042122 A042123 A042124

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved