A056979 - OEIS

%I #21 Sep 24 2015 10:52:23

%S 0,0,0,0,1,0,0,0,0,1,1,0,1,0,0,0,0,0,0,1,2,1,1,0,0,1,1,0,1,0,0,0,0,0,

%T 0,0,1,0,0,1,1,2,2,1,2,1,1,0,0,0,0,1,2,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0,

%U 1,0,0,0,0,1,1,0,1,0,0,1,1,1,1,2,3,2,2,1,1,2,2,1,2,1,1,0,0,0,0,0,1,0

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

%C a(n) = A213629(n,5) for n > 4. - _Reinhard Zumkeller_, Jun 17 2012

%H Reinhard Zumkeller, <a href="/A056979/b056979.txt">Table of n, a(n) for n = 1..10000</a>

%H J.-P. Allouche, J. Shallit, <a href="http://www.math.jussieu.fr/~allouche/kreg2.ps">The Ring of k-regular Sequences II</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitBlock.html">Digit Block</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(2n) = a(n), a(2n+1) = a(n) + [n congruent to 2 mod 4]. - _Ralf Stephan_, Aug 22 2003

%t a[1] = a[2] = 0; a[n_] := a[n] = If[EvenQ[n], a[n/2], a[(n - 1)/2] + Boole[Mod[(n - 1)/2, 4] == 2]]; Table[a[n], {n, 1, 102}] (* _Jean-François Alcover_, Oct 22 2012, after _Ralf Stephan_ *)

%o (Haskell)

%o import Data.List (tails, isPrefixOf)

%o a056979 = sum . map (fromEnum . ([1,0,1] `isPrefixOf`)) .

%o                     tails . a030308_row

%o -- _Reinhard Zumkeller_, Jun 17 2012

%o (PARI) a(n) = hammingweight(bitnegimply(bitand(n, n>>2), n>>1));

%o vector(102, i, a(i))  \\ _Gheorghe Coserea_, Sep 17 2015

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

%K nonn,easy

%O 1,21

%A _Eric W. Weisstein_