A056976 - OEIS

%I #18 May 11 2019 17:17:05

%S 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,

%T 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,

%U 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

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

%H Gheorghe Coserea, <a href="/A056976/b056976.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t 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 *)

%t Table[SequenceCount[IntegerDigits[n,2],{0,1,0},Overlaps->True],{n,120}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 11 2019 *)

%o (PARI)

%o a(n) = {

%o   if (n < 10, return(0));

%o   my(k = logint(n,2) - 1);

%o   hammingweight(bitnegimply(n>>1, bitor(n, n >> 2))) - !bittest(n,k)

%o };

%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 1,42

%A _Eric W. Weisstein_