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 A101080 Table of Hamming distances between binary vectors representing i and j, for i >= 0, j >= 0, read by antidiagonals. 17
 0, 1, 1, 1, 0, 1, 2, 2, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 0, 2, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 2, 1, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 1, 2, 2, 1, 0, 1, 2, 2, 1, 2, 2, 3, 3, 2, 2, 3, 3, 1, 1, 3, 3, 2, 2, 3, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS a(n,0) = a(0,n) = A000120(n). LINKS Alois P. Heinz, Antidiagonals n = 0..200, flattened FORMULA a(i,j) = A000120(A003987(i,j)). EXAMPLE a(3,5) = 2 because the binary Hamming distance (number of differing bits) between ...0011 and ...0101 is 2. From Indranil Ghosh, Mar 31 2017: (Start) Array begins:   0, 1, 1, 2, 1, 2, 2, 3, ...   1, 0, 2, 1, 2, 1, 3, 2, ...   1, 2, 0, 1, 2, 3, 1, 2, ...   2, 1, 1, 0, 3, 2, 2, 1, ...   1, 2, 2, 3, 0, 1, 1, 2, ...   2, 1, 3, 2, 1, 0, 2, 1, ...   2, 3, 1, 2, 1, 2, 0, 1, ...   3, 2, 2, 1, 2, 1, 1, 0, ...   ... Triangle formed when the array is read by antidiagonals:   0;   1, 1;   1, 0, 1;   2, 2, 2, 2;   1, 1, 0, 1, 1;   2, 2, 1, 1, 2, 2;   2, 1, 2, 0, 2, 1, 2;   3, 3, 3, 3, 3, 3, 3, 3;   ... (End) MAPLE H:= (i, j)-> add(v, v=convert(Bits[Xor](i, j), base, 2)): seq(seq(H(n, d-n), n=0..d), d=0..20);  # Alois P. Heinz, Nov 18 2015 MATHEMATICA a[i_, j_] := Total[IntegerDigits[BitXor[i, j], 2]]; Table[a[i-j, j], {i, 0, 20}, {j, 0, i}] // Flatten (* Jean-François Alcover, Apr 07 2016 *) PROG (PARI) b(n) = if(n<1, 0, b(n\2) + n%2); tabl(nn) = {for(n=0, nn, for(k=0, n, print1(b(bitxor(k, n - k)), ", "); ); print(); ); }; tabl(20) \\ Indranil Ghosh, Mar 31 2017 (Python) for n in range(20):     print([bin(k^(n - k))[2:].count("1") for k in range(n + 1)]) # Indranil Ghosh, Mar 31 2017 CROSSREFS Cf. A000120, A003987. Sequence in context: A321858 A334235 A230415 * A130836 A279185 A161385 Adjacent sequences:  A101077 A101078 A101079 * A101081 A101082 A101083 KEYWORD easy,nonn,tabl AUTHOR Marc LeBrun, Nov 29 2004 STATUS approved

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Last modified June 19 12:43 EDT 2021. Contains 345129 sequences. (Running on oeis4.)