A098458 -id:A098458 - cp's OEIS frontend

1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1

Offset: 1

John W. Layman, Sep 08 2004

We define the Farey Bisection Expansion (FBE) of the nonnegative real number x to be the sequence {a(n)} of 0's and 1's determined as follows. Set na(0)=0, da(0)=1, nb(0)=1 and db(0)=0. For n=1, 2, 3,..., set num=na(n-1)+nb(n-1) and den=da(n-1)+db(n-1); if xA010121.

			G.f. = x + x^2 + x^4 + x^6 + x^7 + x^8 + x^9 + x^11 + x^13 + x^14 + x^15 + ...

N. J. A. Sloane, Stern-Brocot or Farey Tree
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

Cf. A010121, A097853, A098458, A131372.

&cat [[1, 1, 0, 1, 0, 1, 1]^^20]; // Wesley Ivan Hurt, Jul 11 2016

seq(op([1, 1, 0, 1, 0, 1, 1]), n=0..20); # Wesley Ivan Hurt, Jul 11 2016

LinearRecurrence[{0, 0, 0, 0, 0, 0, 1},{1, 1, 0, 1, 0, 1, 1},105] (* Ray Chandler, Aug 26 2015 *)

{a(n) = [1, 1, 0, 1, 0, 1, 1][(n-1)%7+1]}; /* Michael Somos, Dec 26 2016 */

From Wesley Ivan Hurt, Jul 11 2016: (Start)
G.f.: x * (1 + x + x^3 + x^5 + x^6) / (1 - x^7).
a(n) = a(n-7) for n>7.
a(n) = 1 - Sum_{k=1..4} floor((n + k)/7)*(-1)^k. (End)
a(n+1) = (-1)^(mod(mod(n, 7), 3)>0) * A131372(n). - Michael Somos, Dec 26 2016

cp's OEIS Frontend

A098457 Farey Bisection Expansion of sqrt(7).

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