A042798 - OEIS

%I #18 Sep 08 2022 08:44:55

%S 30,61,3690,7441,450150,907741,54914610,110736961,6699132270,

%T 13509001501,817239222330,1647987446161,99696485991990,

%U 201040959430141,12162154051800450,24525349063031041,1483683097833662910,2991891544730356861,180997175781655074570

%N Numerators of continued fraction convergents to sqrt(930).

%H Vincenzo Librandi, <a href="/A042798/b042798.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 122, 0, -1).

%F G.f.: (30 +61*x +30*x^2 -x^3)/(1 -122*x^2 +x^4), - _Vincenzo Librandi_, Dec 05 2013

%F a(n) = 122*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 05 2013

%t Numerator[Convergents[Sqrt[930], 30]] (* _Harvey P. Dale_, Apr 27 2012 *)

%t CoefficientList[Series[(30 + 61 x + 30 x^2 - x^3)/(1 - 122 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 05 2013 *)

%o (Magma) I:=[30, 61, 3690, 7441]; [n le 4 select I[n] else 122*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 05 2013

%Y Cf. A042799.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 05 2013