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%I #39 Dec 14 2023 05:38:01
%S 1,10,100,1001,10010,100100,1001001,10010010,100100100,1001001001,
%T 10010010010,100100100100,1001001001001,10010010010010,
%U 100100100100100,1001001001001001,10010010010010010,100100100100100100,1001001001001001001,10010010010010010010
%N Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,0,0.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,0,1,-10).
%F From _Paul Barry_, Apr 16 2005: (Start)
%F G.f.: 1/((1-x^3)*(1-10*x)).
%F a(n) = 10*a(n-1) + a(n-3) - 10*a(n-4).
%F a(n) = Sum_{k=0..floor(n/3)} 10^(n-3k), with offset 0.
%F a(n) = Sum_{k=0..n} 10^k*(cos(2*Pi*(n-k)/3 + Pi/3)/3 + sqrt(3)*sin(2*Pi*(n-k)/3 + Pi/3)/3 + 1/3)), with offset 0. (End)
%F a(n) = round( (100/999)*10^n ). - _Tani Akinari_, Jul 15 2014
%t With[{c = PadLeft[{}, 21, {1, 0, 0}]}, Table[FromDigits[Take[c, n]], {n, 20}]] (* _Harvey P. Dale_, Oct 03 2011 *)
%o (Python) print([100*10**n//999 for n in range(1,50)]) # _Karl V. Keller, Jr._, Oct 05 2021
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_