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A086694 A run of 2^n 1's followed by a run of 2^n 0's, for n=0, 1, 2, ... 2
1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

First differences of A006165 and, likely, of A078881.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

FORMULA

a(n) = 1-A079944(n-1) = 2-A079882(n-1) = A080791(n+1)-A083661(n+1).

a(n) = 1 - floor(log_2(4*(n+1)/3)) + floor(log_2(n+1)).

a(1) = 1, a(2) = 0, a(2n+1) = a(n), a(2n) = a(n-1).

G.f.: Sum_{k>=1} (x^(2^k)-x^(3*2^(k-1)))/(x-x^2). - Robert Israel, Jul 27 2017

G.f.: g(x) = (1/(1 - x))*( Sum_{n >= 1} x^(2^n-1) (1 - x^2^(n-1) ). Functional equation: g(x) = x + x*(1+x)*g(x^2). - Wolfgang Hintze, Aug 05 2017

MAPLE

seq(op([1$(2^n), 0$(2^n)]), n=0..6); # Robert Israel, Jul 27 2017

MATHEMATICA

Table[{PadRight[{}, 2^n, 1], PadRight[{}, 2^n, 0]}, {n, 0, 5}]//Flatten (* Harvey P. Dale, May 29 2017 *)

Table[{Array[1&, 2^n], Array[0&, 2^n]}, {n, 0, 5}]//Flatten (* Wolfgang Hintze, Jul 27 2017 *)

PROG

(PARI) a(n)=if(n<3, if(n<2, 1, 0), if(n%2==0, a(n/2-1), a((n-1)/2)))

CROSSREFS

Cf. A005942, A079944.

Sequence in context: A118175 A179762 A120526 * A093317 A127253 A117944

Adjacent sequences:  A086691 A086692 A086693 * A086695 A086696 A086697

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Sep 12 2003

STATUS

approved

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Last modified October 16 09:16 EDT 2018. Contains 316262 sequences. (Running on oeis4.)