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%I #33 Sep 08 2022 08:45:57
%S 311,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,
%T 622,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,
%U 622,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,622,1,76,1,622
%N Continued fraction expansion of 46*sqrt(46).
%H Vincenzo Librandi, <a href="/A190567/b190567.txt">Table of n, a(n) for n = 0..1000</a>
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F G.f.: (311+x+76*x^2+x^3+311*x^4)/(1-x^4).
%F a(n) = 1+3*(1+(-1)^n)*(116+91*i^n)/2 with n>0, i=sqrt(-1) and a(0)=311.
%F a(n) = (-1513*(n mod 4)+575*((n+1) mod 4)+125*((n+2) mod 4)+2213*((n+3) mod 4))/12 for n>0.
%F a(n) = a(n-4), n>=5. - _Vincenzo Librandi_, Jun 14 2013
%t ContinuedFraction[46 Sqrt[46], 80] (* or *) PadRight[{311}, 80, {622, 1, 76, 1}]
%t CoefficientList[Series[(311 + x + 76 x^2 + x^3 + 311 x^4) / (1 - x^4), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 14 2013 *)
%o (Magma) [311] cat &cat[ [1,76,1,622]: n in [1..18] ];
%o (PARI) a(n)=if(n,[622,1,76,1][n%4+1],311) \\ _Charles R Greathouse IV_, May 13 2011
%o (Magma) I:=[311,1,76,1,622]; [n le 5 select I[n] else Self(n-4): n in [1..80]]; // _Vincenzo Librandi_, Jun 14 2013
%Y Cf. A010136; A040005, A040021, A010186, A040201, A040324, A040489, A040968.
%K nonn,cofr,easy
%O 0,1
%A _Bruno Berselli_, May 13 2011
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