%I #19 Sep 08 2022 08:44:55
%S 27,55,577,1209,65863,132935,1395213,2923361,159256707,321436775,
%T 3373624457,7068685689,385082651663,777233989015,8157422541813,
%U 17092079072641,931129692464427,1879351464001495
%N Numerators of continued fraction convergents to sqrt(755).
%H Vincenzo Librandi, <a href="/A042454/b042454.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 2418, 0, 0, 0, -1).
%F G.f.: (27 +55*x +577*x^2 +1209*x^3 +577*x^4 -55*x^5 +27* x^6 -x^7)/(1 -2418*x^4 +x^8). - _Vincenzo Librandi_, Nov 25 2013
%F a(n) = 2418*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 25 2013
%t Numerator[Convergents[Sqrt[755], 40]] (* _Harvey P. Dale_, Feb 25 2012 *)
%t CoefficientList[Series[(27 + 55 x + 577 x^2 + 1209 x^3 + 577 x^4 - 55 x^5 + 27 x^6 - x^7)/(1 - 2418 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 25 2013 *)
%o (Magma) I:=[27, 55, 577, 1209, 65863, 132935, 1395213, 2923361]; [n le 8 select I[n] else 2418*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 25 2013
%Y Cf. A042455.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
|