A276254 With respect to the dictionary ordering of words over the alphabet {a,b}, i.e., e,a,b,aa,ab,ba,bb,aaa,..., the sequence is the characteristic function of the language of words that have no consecutive b's.

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

Offset

0

References

R. G. Underwood, Fundamentals of Hopf Algebras, UTX, Springer, 2015, page 61.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..16383

Michel Rigo and Robert Underwood, A Class of Automatic Sequences, arXiv:1712.10259 [cs.FL], 2017-2018.

Formula

a(n) = 0 iff A007931(n) contains two (or more) consecutive 2's. - Alois P. Heinz, Aug 26 2016

Maple

a:= proc(n) local m, r, d; m, r:= n, 1;
      while m>0 do d:= irem(m, 2, 'm');
        if d=0 then if r=0 then return 0 fi;
          m:= m-1 fi; r:=d;
      od; 1
    end:
seq(a(n), n=0..200);  # Alois P. Heinz, Aug 25 2016

Mathematica

a[n_] := Module[{m, r, d}, {m, r} = {n, 1}; While[m > 0, {m, d} = QuotientRemainder[m, 2]; If[d == 0, If[r == 0, Return[0]]; m = m-1]; r = d]; 1];
Table[a[n], {n, 0, 200}] (* Jean-François Alcover, Mar 24 2018, after Alois P. Heinz *)

Crossrefs

Cf. A007931.

Sequence in context: A336477 A190230 A141679 * A303300 A249865 A152904

Adjacent sequences: A276251 A276252 A276253 * A276255 A276256 A276257

Keyword

nonn

Author

Robert G. Underwood, Aug 25 2016

Extensions

More terms from Alois P. Heinz, Aug 25 2016

Status

approved