A042566 - OEIS

%I #16 Jun 03 2024 11:59:51

%S 28,57,3220,6497,367052,740601,41840708,84422017,4769473660,

%T 9623369337,543678156532,1096979682401,61974540370988,125046060424377,

%U 7064553924136100,14254153908696577,805297172811144412

%N Numerators of continued fraction convergents to sqrt(812).

%H Vincenzo Librandi, <a href="/A042566/b042566.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, 114, 0, -1).

%F G.f.: (28 +57*x +28*x^2 -x^3)/(1 -114*x^2 +x^4). - _Vincenzo Librandi_, Nov 28 2013

%F a(n) = 114*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 28 2013

%t Numerator[Convergents[Sqrt[812], 30]] (* or *) CoefficientList[Series[(28 + 57 x + 28 x^2 - x^3)/(1 - 114 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 28 2013 *)

%t LinearRecurrence[{0,114,0,-1},{28,57,3220,6497},20] (* _Harvey P. Dale_, Jun 03 2024 *)

%o (Magma) I:=[28, 57, 3220, 6497]; [n le 4 select I[n] else 114*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 28 2013

%Y Cf. A042567.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.