This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056978 #25 Feb 16 2025 08:32:43 %S A056978 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, %T A056978 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, %U A056978 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 %N A056978 Number of blocks of {1, 0, 0} in binary expansion of n. %C A056978 a(n) = A213629(n,4) for n > 3. - _Reinhard Zumkeller_, Jun 17 2012 %H A056978 Reinhard Zumkeller, <a href="/A056978/b056978.txt">Table of n, a(n) for n = 1..10000</a> %H A056978 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitBlock.html">Digit Block</a> %F A056978 a(2n) = a(n) + [n congruent to 2 mod 4], a(2n+1) = a(n). - _Ralf Stephan_, Aug 22 2003 %t A056978 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_ *) %t A056978 Table[SequenceCount[IntegerDigits[n,2],{1,0,0}],{n,120}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Dec 01 2016 *) %o A056978 (Haskell) %o A056978 import Data.List (tails, isPrefixOf) %o A056978 a056978 = sum . map (fromEnum . ([0,0,1] `isPrefixOf`)) . %o A056978 tails . a030308_row %o A056978 -- _Reinhard Zumkeller_, Jun 17 2012 %o A056978 (PARI) %o A056978 a(n) = hammingweight(bitnegimply(n>>2, bitor(n>>1, n))); \\ _Gheorghe Coserea_, Sep 08 2015 %Y A056978 Cf. A014082, A056974, A056975, A056976, A056977, A056978, A056979, A056980. %K A056978 nonn,easy %O A056978 1,36 %A A056978 _Eric W. Weisstein_