A056976 Number of blocks of {0, 1, 0} in the binary expansion of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0

Offset

1,42

Links

Gheorghe Coserea, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Digit Block

Formula

a(2n) = a(n) + [n>1 and n congruent to 1 mod 4], a(2n+1) = a(n). - Ralf Stephan, Aug 22 2003

Mathematica

a[n_, bits_] := (idn = IntegerDigits[n, 2]; ln = Length[idn]; lb = Length[bits]; For[cnt = 0; k = 1, k <= ln - lb + 1, k++, If[idn[[k ;; k + lb - 1]] == bits, cnt++]]; cnt); Table[ a[n, {0, 1, 0}], {n, 1, 102} ] (* Jean-François Alcover, Oct 23 2012 *)
Table[SequenceCount[IntegerDigits[n, 2], {0, 1, 0}, Overlaps->True], {n, 120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 11 2019 *)

Prog

(PARI)
a(n) = {
  if (n < 10, return(0));
  my(k = logint(n, 2) - 1);
  hammingweight(bitnegimply(n>>1, bitor(n, n >> 2))) - !bittest(n, k)
};
vector(102, i, a(i))  \\ Gheorghe Coserea, Sep 17 2015

Crossrefs

Cf. A014082, A056974, A056975, A056976, A056977, A056978, A056979, A056980.

Sequence in context: A368844 A377336 A181563 * A279281 A342465 A124749

Adjacent sequences: A056973 A056974 A056975 * A056977 A056978 A056979

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved