A041966 - OEIS

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

%S 22,45,2002,4049,180158,364365,16212218,32788801,1458919462,

%T 2950627725,131286539362,265523706449,11814329623118,23894182952685,

%U 1063158379541258,2150210942035201,95672439829090102,193495090600215405

%N Numerators of continued fraction convergents to sqrt(506).

%H Vincenzo Librandi, <a href="/A041966/b041966.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, 90, 0, -1).

%F G.f.: (22 + 45*x + 22*x^2 - x^3)/(1 - 90*x^2 + x^4). - _Vincenzo Librandi_, Nov 12 2013

%F a(n) = 90*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 12 2013

%t Numerator[Convergents[Sqrt[506], 30]] (* or *) CoefficientList[Series[(22 + 45 x + 22 x^2 - x^3)/(1 - 90 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 12 2013 *)

%o (Magma) I:=[22,45,2002,4049]; [n le 4 select I[n] else 90*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 12 2013

%Y Cf. A041967.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.