A041723 - OEIS

%I #19 Sep 08 2022 08:44:54

%S 1,1,2,25,27,52,2003,2055,4058,50751,54809,105560,4066089,4171649,

%T 8237738,103024505,111262243,214286748,8254158667,8468445415,

%U 16722604082,209139694399,225862298481,435001992880,16755938027921,17190940020801,33946878048722

%N Denominators of continued fraction convergents to sqrt(381).

%H Vincenzo Librandi, <a href="/A041723/b041723.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 2030, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-26*x^3-1) / (x^12-2030*x^6+1). - _Colin Barker_, Nov 22 2013

%F a(n) = 2030*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 23 2013

%p convert(sqrt(381), confrac, 30, cvgts): denom(cvgts); # _Wesley Ivan Hurt_, Dec 23 2013

%t Denominator[Convergents[Sqrt[381], 30]] (* _Vincenzo Librandi_, Dec 23 2013 *)

%o (Magma) I:=[1,1,2,25,27,52,2003,2055,4058,50751,54809, 105560]; [n le 12 select I[n] else 2030*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 23 2013

%Y Cf. A041722, A040361.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 22 2013