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

0,8

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).

Links

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

Example

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;
    ...

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

Prog

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

Crossrefs

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

Cf. A002487, A104594, A328564.

Sequence in context: A105166 A321299 A105783 * A268189 A265247 A022879

Adjacent sequences: A326816 A326817 A326818 * A326820 A326821 A326822

Keyword

nonn,tabf,look,base

Author

Rémy Sigrist, Oct 20 2019

Status

approved