%I #16 Sep 08 2022 08:44:54
%S 1,2,7,44,139,322,10443,21208,74067,465610,1470897,3407404,110507825,
%T 224423054,783776987,4927084976,15565031915,36057148806,1169393793707,
%U 2374844736220,8293928002367,52138412750422,164709166253633,381556745257688
%N Denominators of continued fraction convergents to sqrt(270).
%H Vincenzo Librandi, <a href="/A041507/b041507.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 (0,0,0,0,0,10582,0,0,0,0,0,-1).
%F G.f.: -(x^10 -2*x^9 +7*x^8 -44*x^7 +139*x^6 -322*x^5 -139*x^4 -44*x^3 -7*x^2 -2*x -1) / ((x^4 -22*x^2 +1)*(x^8 +22*x^6 +483*x^4 +22*x^2 +1)). - _Colin Barker_, Nov 18 2013
%F a(n) = 10582*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 19 2013
%t Denominator[Convergents[Sqrt[270], 30]] (* _Vincenzo Librandi_, Dec 19 2013 *)
%o (Magma) I:=[1,2,7,44,139,322,10443,21208,74067,465610, 1470897,3407404]; [n le 12 select I[n] else 10582*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Dec 19 2013
%Y Cf. A041506, A040253.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 18 2013