A326819 Irregular triangle read by rows; for n >= 0, the n-th row corresponds to the elements of the set {(n-k) AND k, k = 0..n}, in ascending order (where AND denotes the bitwise AND operator).

0, 0, 0, 1, 0, 0, 1, 2, 0, 2, 0, 1, 3, 0, 0, 1, 2, 4, 0, 2, 4, 0, 1, 3, 4, 5, 0, 4, 0, 1, 2, 5, 6, 0, 2, 6, 0, 1, 3, 7, 0, 0, 1, 2, 4, 8, 0, 2, 4, 8, 0, 1, 3, 4, 5, 8, 9, 0, 4, 8, 0, 1, 2, 5, 6, 8, 9, 10, 0, 2, 6, 8, 10, 0, 1, 3, 7, 8, 9, 11, 0, 8, 0, 1, 2, 4, 9, 10, 12

Offset: 0

Author

Rémy Sigrist, Oct 20 2019

Keywords

• nonn
• tabf
• look
• base

Comments

For any n >= 0, the n-th row:

- has sum A328564(n),

- has apparently length A002487(n+1),

- has first element 0,

- has last element A104594(n).

Examples

			Table begins:
    0;
    0;
    0, 1;
    0;
    0, 1, 2;
    0, 2;
    0, 1, 3;
    0;
    0, 1, 2, 4;
    0, 2, 4;
    0, 1, 3, 4, 5;
    0, 4;
    0, 1, 2, 5, 6;
    0, 2, 6;
    0, 1, 3, 7;
    ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..9851 (rows n = 0..512)

Crossrefs

Cf. A326820 (OR variant), A328568 (XOR variant).

Cf. A002487, A104594, A328564.

Programs

Maple

T:= n-> sort([{seq(Bits[And](n-k, k), k=0..n)}[]])[]:
seq(T(n), n=0..30);  # Alois P. Heinz, Oct 20 2019

PARI

row(n) = Set(apply(k -> bitand(n-k, k), [0..n]))