%I #27 Jul 16 2021 01:34:57
%S 0,1,1,0,1,2,0,0,1,2,2,-1,0,1,0,0,1,2,2,1,2,3,-1,-1,0,1,1,-1,0,1,0,0,
%T 1,2,2,1,2,3,1,1,2,3,3,-2,-1,0,-1,-1,0,1,1,0,1,2,-1,-1,0,1,1,-1,0,1,0,
%U 0,1,2,2,1,2,3,1,1,2,3,3,0,1,2,1,1,2,3,3,2
%N a(n) is the sum of digits of n in signed binary nonadjacent form.
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational - Ideas, Algorithms, Source Code</a>, 2011, Springer, pp. 61-62.
%H Helmut Prodinger, <a href="http://www.emis.de/journals/INTEGERS/papers/a8/a8.Abstract.html">On binary representations of integers with digits -1,0,1</a>, Integers 0 (2000), #A08.
%F a(n) = hammingweight(A184615(n)) - hammingweight(A184616(n)). - _Joerg Arndt_, Jun 13 2020
%t BBN[a_] := Module[{n = a, b}, b = IntegerDigits[n, 2]; b = Prepend[b, 0];
%t l = Length[b];
%t Do[If[b[[i]] == 2, b[[i]] = 0; b[[i - 1]]++,
%t If[b[[i]] == 1,
%t If[b[[i + 1]] == 1, b[[i - 1]]++; b[[i]] = 0;
%t b[[i + 1]] = -1]]], {i, l - 1, 2, -1}];
%t If[b[[1]] == 0, b = Delete[b, 1]]; b]
%t Table[a = BBN[i]; sod = 0; l = Length[a];
%t Do[sod = sod + a[[j]], {j, 1, l}]; sod, {i, 0, 83}]
%o (PARI)
%o bin2naf(x)=
%o { /* Compute (nonadjacent) signed binary representation of x: */
%o local(xh, x3, c, np, nm);
%o xh = x >> 1;
%o x3 = x + xh;
%o c = bitxor(xh, x3);
%o np = bitand(x3, c); /* bits == +1 */
%o nm = bitand(xh, c); /* bits == -1 */
%o return([np, nm]); /* np-nm==x */
%o }
%o a(n) = my(b=bin2naf(n)); return(hammingweight(b[1])-hammingweight(b[2]));
%o vector(99,n,a(n-1)) \\ _Joerg Arndt_, Jun 13 2020
%Y Cf. A000120, A001045, A007302, A184615, A184616.
%K base,easy,sign
%O 0,6
%A _Lei Zhou_, May 16 2020