A056980 Number of blocks of {1, 1, 0} in binary expansion of n.

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

Offset

1,54

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Digit Block.

Formula

a(2n) = a(n) + [n congruent to 3 mod 4], a(2n+1) = a(n). - Ralf Stephan, Aug 22 2003

a(n) = A213629(n,6) for n > 5. - 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] == 3]]; Table[a[n], {n, 1, 102}] (* Jean-François Alcover, Oct 22 2012, after Ralf Stephan *)

Prog

(Haskell)
import Data.List (tails, isPrefixOf)
a056980 = sum . map (fromEnum . ([0, 1, 1] `isPrefixOf`)) .
                    tails . a030308_row
-- Reinhard Zumkeller, Jun 17 2012
(PARI)
a(n) = hammingweight(bitnegimply(bitand(n>>1, n>>2), n));
vector(102, i, a(i))  \\  Gheorghe Coserea, Sep 07 2015

Crossrefs

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

Cf. A213629.

Sequence in context: A176046 A172090 A037912 * A268643 A005094 A121372

Adjacent sequences: A056977 A056978 A056979 * A056981 A056982 A056983

Keyword

nonn,easy,base

Author

Eric W. Weisstein

Status

approved