A042275 - OEIS

%I #20 Sep 08 2022 08:44:55

%S 1,1,3,4,203,207,617,824,41817,42641,127099,169740,8614099,8783839,

%T 26181777,34965616,1774462577,1809428193,5393318963,7202747156,

%U 365530676763,372733423919,1110997524601,1483730948520,75297544950601,76781275899121

%N Denominators of continued fraction convergents to sqrt(663).

%H Vincenzo Librandi, <a href="/A042275/b042275.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, 206, 0, 0, 0, -1).

%F G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-206*x^4+1). - _Colin Barker_, Dec 06 2013

%F a(n) = 206*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Jan 19 2014

%p convert(sqrt(663),confrac,30,cvgts): denom(cvgts); # _Wesley Ivan Hurt_, Dec 07 2013

%t Denominator[Convergents[Sqrt[663], 30]] (* _Vincenzo Librandi_, Jan 19 2014 *)

%o (Magma) I:=[1,1,3,4,203,207,617,824]; [n le 8 select I[n] else 206*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Jan 19 2014

%Y Cf. A042274, A040637.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 06 2013