A056978 Number of blocks of {1, 0, 0} in binary expansion of n.

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

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

a(n) = A213629(n,4) for n > 3. - Reinhard Zumkeller, Jun 17 2012

Links

• Reinhard Zumkeller, 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

Haskell

import Data.List (tails, isPrefixOf)
a056978 = sum . map (fromEnum . ([0,0,1] `isPrefixOf`)) .
                    tails . a030308_row
-- Reinhard Zumkeller, Jun 17 2012

Mathematica

a[1] = a[2] = 0; a[n_] := a[n] = If[OddQ[n], a[(n-1)/2], a[n/2] + Boole[Mod[n/2, 4] == 2]]; Table[a[n], {n, 1, 102}] (* Jean-François Alcover, Oct 22 2012, after Ralf Stephan *)
Table[SequenceCount[IntegerDigits[n,2],{1,0,0}],{n,120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 01 2016 *)

PARI

a(n) = hammingweight(bitnegimply(n>>2, bitor(n>>1, n)));  \\ Gheorghe Coserea, Sep 08 2015

Formula

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