A042863 - OEIS

%I #17 Jun 26 2022 23:39:04

%S 1,31,1923,59644,3699851,114755025,7118511401,220788608456,

%T 13696012235673,424797167914319,26351120422923451,817309530278541300,

%U 50699541997692484051,1572503111458745546881,97545892452439916390673,3025495169137096153657744

%N Denominators of continued fraction convergents to sqrt(963).

%H Vincenzo Librandi, <a href="/A042863/b042863.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, 1924, 0, -1).

%F G.f.: -(x^2 - 31*x - 1) / (x^4 - 1924*x^2 + 1). - _Colin Barker_, Dec 25 2013

%F a(n) = 1924*a(n-2) - a(n-4) for n > 3. - _Vincenzo Librandi_, Dec 25 2013

%t Denominator[Convergents[Sqrt[963], 30]] (* _Vincenzo Librandi_, Dec 25 2013 *)

%o (Magma) I:=[1,31,1923,59644]; [n le 4 select I[n] else 1924*Self(n-2)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Dec 25 2013

%Y Cf. A042862, A040931.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_

%E Additional term from _Colin Barker_, Dec 25 2013