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

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Digit Block

Crossrefs

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

Programs

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 *)

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

Formula

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