A042510 - OEIS

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

%S 27,28,1539,1567,86157,87724,4823253,4910977,270016011,274926988,

%T 15116073363,15391000351,846230092317,861621092668,47373769096389,

%U 48235390189057,2652084839305467,2700320229494524

%N Numerators of continued fraction convergents to sqrt(783).

%H Vincenzo Librandi, <a href="/A042510/b042510.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 (0,56,0,-1).

%F G.f.: (27 + 28*x + 27*x^2 - x^3)/(1 - 56*x^2 + x^4). - _Vincenzo Librandi_, Nov 26 2013

%F a(n) = 56*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 26 2013

%t Numerator[Convergents[Sqrt[783], 30]] (* or *) CoefficientList[Series[(27 + 28 x + 27 x^2 - x^3)/(1 - 56 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 25 2013 *)

%t LinearRecurrence[{0,56,0,-1},{27,28,1539,1567},30] (* _Harvey P. Dale_, Apr 28 2016 *)

%o (Magma) I:=[27, 28, 1539, 1567]; [n le 4 select I[n] else 56*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 26 2013

%Y Cf. A042511.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_