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

1,2

Links

Table of n, a(n) for n=1..20.

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

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

Adjacent sequences: A033143 A033144 A033145 * A033147 A033148 A033149

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved