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A328568
Irregular triangle read by rows; for n >= 0, the n-th row corresponds to the elements of the set {(n-k) XOR k, k = 0..n}, in ascending order (where XOR denotes the bitwise XOR operator).
4
0, 1, 0, 2, 3, 0, 2, 4, 1, 5, 0, 4, 6, 7, 0, 4, 6, 8, 1, 5, 9, 0, 2, 4, 8, 10, 3, 11, 0, 2, 8, 10, 12, 1, 9, 13, 0, 8, 12, 14, 15, 0, 8, 12, 14, 16, 1, 9, 13, 17, 0, 2, 8, 10, 12, 16, 18, 3, 11, 19, 0, 2, 4, 8, 10, 16, 18, 20, 1, 5, 9, 17, 21, 0, 4, 6, 8, 16, 20, 22
OFFSET
0,4
COMMENTS
For any n >= 0, the n-th row:
- has sum A328565(n),
- has apparently length A002487(n+1),
- has first element A135481(n),
- has last element n.
LINKS
EXAMPLE
Table begins:
0;
1;
0, 2;
3;
0, 2, 4;
1, 5;
0, 4, 6;
7;
0, 4, 6, 8;
1, 5, 9;
0, 2, 4, 8, 10;
3, 11;
0, 2, 8, 10, 12;
1, 9, 13;
0, 8, 12, 14;
...
MAPLE
T:= n-> sort([{seq(Bits[Xor](n-k, k), k=0..n)}[]])[]:
seq(T(n), n=0..30); # Alois P. Heinz, Oct 20 2019
MATHEMATICA
Union /@ Table[BitXor[n - k, k], {n, 0, 22}, {k, 0, n}] // Flatten (* George Beck, Jun 09 2023 *)
PROG
(PARI) row(n) = Set(apply(k -> bitxor(n-k, k), [0..n]))
CROSSREFS
Cf. A326819 (AND variant), A326820 (OR variant).
Sequence in context: A024307 A369287 A267852 * A219864 A257844 A194745
KEYWORD
nonn,tabf,look,base
AUTHOR
Rémy Sigrist, Oct 20 2019
STATUS
approved