A033146 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,0,0.

1, 10, 100, 1001, 10010, 100100, 1001001, 10010010, 100100100, 1001001001, 10010010010, 100100100100, 1001001001001, 10010010010010, 100100100100100, 1001001001001001, 10010010010010010, 100100100100100100, 1001001001001001001, 10010010010010010010

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,0,1,-10).

Programs

Mathematica

With[{c = PadLeft[{}, 21, {1, 0, 0}]}, Table[FromDigits[Take[c, n]], {n, 20}]] (* Harvey P. Dale, Oct 03 2011 *)

Python

print([100*10**n//999 for n in range(1,50)]) # Karl V. Keller, Jr., Oct 05 2021

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