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Number of blocks of {0, 0, 1} in binary expansion of n.
9

%I #19 Jun 04 2021 02:33:17

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

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

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

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

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

%F a(2n) = a(n), a(2n+1) = a(n) + [n congruent to 0 mod 4]. - _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, 0, 1}], {n, 1, 102} ] (* _Jean-François Alcover_, Oct 23 2012 *)

%t Table[SequenceCount[IntegerDigits[n,2],{0,0,1}],{n,110}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 26 2019 *)

%Y Cf. A007088 (binary expansion).

%Y Other block counts: A014082, A056974, A056976, A056977, A056978, A056979, A056980.

%K nonn,base,easy

%O 1,73

%A _Eric W. Weisstein_