A042031 - OEIS

%I #19 Sep 05 2022 21:53:35

%S 1,4,5,9,14,23,37,171,7903,31783,39686,71469,111155,182624,293779,

%T 1357740,62749819,252357016,315106835,567463851,882570686,1450034537,

%U 2332605223,10780455429,498233554957,2003714675257,2501948230214,4505662905471,7007611135685

%N Denominators of continued fraction convergents to sqrt(539).

%H Vincenzo Librandi, <a href="/A042031/b042031.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 7940, 0, 0, 0, 0, 0, 0, 0, -1).

%F 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

%F a(n) = 7940*a(n-8) - a(n-16). - _Wesley Ivan Hurt_, Sep 05 2022

%t Denominator[Convergents[Sqrt[539], 30]] (* _Vincenzo Librandi_, Jan 12 2014 *)

%t 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 *)

%Y Cf. A042030, A040515.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 29 2013