login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numerators of continued fraction convergents to sqrt(482).
2

%I #24 May 28 2023 18:29:37

%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