A041920 - OEIS

%I #26 Jul 09 2025 01:54:44

%S 21,22,461,483,20747,21230,445347,466577,20041581,20508158,430204741,

%T 450712899,19360146499,19810859398,415577334459,435388193857,

%U 18701881476453,19137269670310,401447274882653,420584544552963,18065998146107099,18486582690660062

%N Numerators of continued fraction convergents to sqrt(482).

%H Vincenzo Librandi, <a href="/A041920/b041920.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 (0,0,0,966,0,0,0,-1).

%F G.f.: (21 +22*x +461*x^2 +483*x^3 +461*x^4 -22*x^5 +21*x^6 -x^7)/(1 -966*x^4 +x^8). - _Vincenzo Librandi_, Nov 12 2013

%F a(n) = 966*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 12 2013

%t Numerator[Convergents[Sqrt[482], 30]] (* or *) CoefficientList[Series[(21 + 22 x + 461 x^2 + 483 x^3 + 461 x^4 - 22 x^5 + 21 x^6 - x^7)/(1 - 966 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 12 2013 *)

%t LinearRecurrence[{0,0,0,966,0,0,0,-1},{21,22,461,483,20747,21230,445347,466577},30] (* _Harvey P. Dale_, May 28 2023 *)

%o (Magma) I:=[21,22,461,483,20747,21230,445347,466577]; [n le 8 select I[n] else 966*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 12 2013

%Y Cf. A041921, A040460.

%K nonn,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_

%E More terms and second link corrected by _Colin Barker_, Dec 28 2013