A042039 Denominators of continued fraction convergents to sqrt(543).

1, 3, 10, 33, 43, 635, 678, 2669, 8685, 28724, 1329989, 4018691, 13386062, 44176877, 57562939, 850058023, 907620962, 3572920909, 11626383689, 38452071976, 1780421694585, 5379717155731, 17919573161778, 59138436641065, 77058009802843, 1137950573880867

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, 0, 0, 1338674, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -3*x^17 +10*x^16 -33*x^15 +43*x^14 -635*x^13 +678*x^12 -2669*x^11 +8685*x^10 -28724*x^9 -8685*x^8 -2669*x^7 -678*x^6 -635*x^5 -43*x^4 -33*x^3 -10*x^2 -3*x -1) / (x^20 -1338674*x^10 +1). - Colin Barker, Nov 30 2013

a(n) = 1338674*a(n-10) - a(n-20). - Wesley Ivan Hurt, Sep 05 2022

Mathematica

Denominator[Convergents[Sqrt[543], 30]] (* Vincenzo Librandi, Jan 12 2014 *)

Crossrefs

Cf. A042038, A040519.

Sequence in context: A174573 A126183 A174798 * A080697 A316404 A333027

Adjacent sequences: A042036 A042037 A042038 * A042040 A042041 A042042

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 30 2013

Status

approved