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A033146
Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,0,0.
1
1, 10, 100, 1001, 10010, 100100, 1001001, 10010010, 100100100, 1001001001, 10010010010, 100100100100, 1001001001001, 10010010010010, 100100100100100, 1001001001001001, 10010010010010010, 100100100100100100, 1001001001001001001, 10010010010010010010
OFFSET
1,2
FORMULA
From Paul Barry, Apr 16 2005: (Start)
G.f.: 1/((1-x^3)*(1-10*x)).
a(n) = 10*a(n-1) + a(n-3) - 10*a(n-4).
a(n) = Sum_{k=0..floor(n/3)} 10^(n-3k), with offset 0.
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)
a(n) = round( (100/999)*10^n ). - Tani Akinari, Jul 15 2014
MATHEMATICA
With[{c = PadLeft[{}, 21, {1, 0, 0}]}, Table[FromDigits[Take[c, n]], {n, 20}]] (* Harvey P. Dale, Oct 03 2011 *)
PROG
(Python) print([100*10**n//999 for n in range(1, 50)]) # Karl V. Keller, Jr., Oct 05 2021
CROSSREFS
Sequence in context: A283013 A283057 A283079 * A282907 A281730 A282954
KEYWORD
nonn,base,easy
STATUS
approved