A042858 - OEIS

%I #19 Jun 19 2023 06:40:35

%S 30,31,1890,1921,117150,119071,7261410,7380481,450090270,457470751,

%T 27898335330,28355806081,1729246700190,1757602506271,107185397076450,

%U 108942999582721,6643765372039710,6752708371622431,411806267669385570,418558976041008001,25525344830129865630

%N Numerators of continued fraction convergents to sqrt(960).

%H Vincenzo Librandi, <a href="/A042858/b042858.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 (0,62,0,-1).

%F G.f.: (30 + 31*x + 30*x^2 - x^3)/(1 - 62*x^2 + x^4). - _Vincenzo Librandi_, Dec 08 2013

%F a(n) = 62*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 08 2013

%t Numerator[Convergents[Sqrt[960], 30]] (* _Vincenzo Librandi_, Dec 07 2013 *)

%t CoefficientList[Series[(30 + 31 x + 30 x^2 - x^3)/(1 - 62 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 08 2013 *)

%o (Magma) I:=[ 30, 31, 1890, 1921]; [n le 4 select I[n] else 62*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 08 2013

%Y Cf. A042859.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Dec 08 2013