A042031 Denominators of continued fraction convergents to sqrt(539).

1, 4, 5, 9, 14, 23, 37, 171, 7903, 31783, 39686, 71469, 111155, 182624, 293779, 1357740, 62749819, 252357016, 315106835, 567463851, 882570686, 1450034537, 2332605223, 10780455429, 498233554957, 2003714675257, 2501948230214, 4505662905471, 7007611135685

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, 7940, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -4*x^13 +5*x^12 -9*x^11 +14*x^10 -23*x^9 +37*x^8 -171*x^7 -37*x^6 -23*x^5 -14*x^4 -9*x^3 -5*x^2 -4*x -1) / (x^16 -7940*x^8 +1). - Colin Barker, Nov 29 2013

a(n) = 7940*a(n-8) - a(n-16). - Wesley Ivan Hurt, Sep 05 2022

Mathematica

Denominator[Convergents[Sqrt[539], 30]] (* Vincenzo Librandi, Jan 12 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 7940, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 4, 5, 9, 14, 23, 37, 171, 7903, 31783, 39686, 71469, 111155, 182624, 293779, 1357740}, 30] (* Harvey P. Dale, May 25 2015 *)

Crossrefs

Cf. A042030, A040515.

Sequence in context: A274282 A347553 A000285 * A041493 A352321 A250474

Adjacent sequences: A042028 A042029 A042030 * A042032 A042033 A042034

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 29 2013

Status

approved