login
Denominators of continued fraction convergents to sqrt(741).
2

%I #16 Jun 13 2015 00:49:45

%S 1,4,5,9,122,2205,28787,30992,59779,270108,14645611,58852552,73498163,

%T 132350715,1794057458,32425384959,423324061925,455749446884,

%U 879073508809,3972043482120,215369421543289,865449729655276,1080819151198565,1946268880853841

%N Denominators of continued fraction convergents to sqrt(741).

%H Vincenzo Librandi, <a href="/A042427/b042427.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,14705390,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^18 -4*x^17 +5*x^16 -9*x^15 +122*x^14 -2205*x^13 +28787*x^12 -30992*x^11 +59779*x^10 -270108*x^9 -59779*x^8 -30992*x^7 -28787*x^6 -2205*x^5 -122*x^4 -9*x^3 -5*x^2 -4*x -1) / (x^20 -14705390*x^10 +1). - _Colin Barker_, Dec 12 2013

%F a(n) = 14705390*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Jan 22 2014

%t Denominator[Convergents[Sqrt[741], 30]] (* _Harvey P. Dale_, Dec 31 2012 *)

%t CoefficientList[Series[-(x^18 - 4 x^17 + 5 x^16 - 9 x^15 + 122 x^14 - 2205 x^13 + 28787 x^12 - 30992 x^11 + 59779 x^10 - 270108 x^9 - 59779 x^8 - 30992 x^7 - 28787 x^6 - 2205 x^5 - 122 x^4 - 9 x^3 - 5 x^2 - 4 x - 1)/(x^20 - 14705390 x^10 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 22 2014 *)

%Y Cf. A042426, A040713.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 12 2013