A341259 Number of 0's in n-th word defined at A341258.

1, 0, 2, 1, 1, 3, 0, 2, 2, 2, 4, 1, 1, 3, 1, 3, 3, 3, 5, 0, 2, 2, 2, 4, 2, 2, 4, 2, 4, 4, 4, 6, 1, 1, 3, 1, 3, 3, 3, 5, 1, 3, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 7, 0, 2, 2, 2, 4, 2, 2, 4, 2, 4, 4, 4, 6, 2, 2, 4, 2, 4, 4, 4, 6, 2, 4, 4, 4, 6, 4, 4, 6, 4, 6, 6, 6

Offset: 1

Author

Clark Kimberling, Mar 16 2021

Keywords

• nonn

Comments

The number of 1's in the n-th word is given by A117479.

Crossrefs

Cf. A117479, A341258.

Appears to be A200649 - 1.

Programs

Mathematica

z = 200; r = (1 + Sqrt[5])/2;
s = Table[Floor[r*n], {n, 1, z}]; t = Complement[Range[Max[s]], s];
s1[n_] := Length[Intersection[Range[n - 1], s]];
t1[n_] := n - 1 - s1[n];
w[1] = {0}; w[t[[1]]] = {1};
w[n_] := If[MemberQ[s, n], Join[{0}, w[s1[n]]], Join[{1}, w[t1[n]]]]
tt = Table[w[n], {n, 1, z}] (* A341258 *)
c[n_] := Count[tt[[n]], 0]; Table[c[n], {n, 1, z}]  (* A341259 *)
d[n_] := Count[tt[[n]], 1]; Table[d[n], {n, 1, z}]  (* A117479 *)