A056977 Number of blocks of {0, 1, 1} in binary expansion of n.

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

Offset

1,91

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), a(2n+1) = a(n) + [n>1 and n congruent to 1 mod 4]. - 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, 1}], {n, 1, 102} ] (* Jean-François Alcover, Oct 23 2012 *)
Table[SequenceCount[IntegerDigits[n, 2], {0, 1, 1}], {n, 120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 03 2019 *)

Prog

(PARI)
a(n) = {
  if (n < 11, return(0));
  my(k = logint(n, 2) - 1);
  hammingweight(bitnegimply(bitand(n>>1, 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: A277007 A160380 A122433 * A309144 A085425 A355685

Adjacent sequences: A056974 A056975 A056976 * A056978 A056979 A056980

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved