A042081 - OEIS

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

%S 1,1,3,4,187,191,569,760,35529,36289,108107,144396,6750323,6894719,

%T 20539761,27434480,1282525841,1309960321,3902446483,5212406804,

%U 243673159467,248885566271,741444292009,990329858280,46296617772889,47286947631169

%N Denominators of continued fraction convergents to sqrt(564).

%H Vincenzo Librandi, <a href="/A042081/b042081.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,190,0,0,0,-1).

%F G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-190*x^4+1). - _Colin Barker_, Dec 01 2013

%F a(n) = 190*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Jan 14 2014

%t Denominator[Convergents[Sqrt[564], 30]] (* _Harvey P. Dale_, Nov 08 2011 *)

%t CoefficientList[Series[(1 + x - x^2) (x^4 + 4 x^2 + 1)/(x^8 - 190 x^4 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jan 14 2014 *)

%o (Magma) I:=[1,1,3,4,187,191,569,760]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Jan 14 2014

%Y Cf. A042080, A040540.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 01 2013