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%I #15 Mar 09 2014 12:36:42
%S 1,1,2,2,3,4,5,7,9,13,17,22,29,39,51,68,90,119,158,209,277,367,486,
%T 644,853,1130,1497,1983,2627,3480,4610,6107,8090,10717,14197,18807,
%U 24914,33004,43721,57918,76725,101639,134643,178364,236282,313007,414646,549289,727653,963935,1276942,1691588,2240877,2968530,3932465
%N a(n) = round(r^n) where r is the smallest Pisot number (real root r=1.3247179.. of x^3-x-1).
%H Vincenzo Librandi, <a href="/A205579/b205579.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein: <a href="http://mathworld.wolfram.com/PisotNumber.html">Pisot Number</a>.
%F G.f.: (1+x+x^2+x^9+x^10-x^12)/(1-x^2-x^3).
%t CoefficientList[Series[(1+x+x^2+x^9+x^10-x^12)/(1-x^2-x^3),{x,0,100}],x] (* _Vincenzo Librandi_, Aug 19 2012 *)
%o (PARI)
%o default(realprecision, 110);
%o default(format, "g.15");
%o r=real(polroots(x^3-x-1)[1])
%o v=vector(66, n, round(r^(n-1)) )
%o (PARI) Vec((1+x+x^2+x^9+x^10-x^12)/(1-x^2-x^3)+O(x^66))
%Y Cf. A112639 (definition using floor() instead of round()).
%Y Cf. A060006 (decimal expansion of r=1.32471795724475...).
%Y Cf. A051016, A051017.
%K nonn
%O 0,3
%A _Joerg Arndt_, Jan 29 2012
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