A326820 Irregular triangle read by rows; for n >= 0, the n-th row corresponds to the elements of the set {(n-k) OR k, k = 0..n}, in ascending order (where OR denotes the bitwise OR operator).

0, 1, 1, 2, 3, 2, 3, 4, 3, 5, 3, 5, 6, 7, 4, 6, 7, 8, 5, 7, 9, 5, 6, 7, 9, 10, 7, 11, 6, 7, 10, 11, 12, 7, 11, 13, 7, 11, 13, 14, 15, 8, 12, 14, 15, 16, 9, 13, 15, 17, 9, 10, 13, 14, 15, 17, 18, 11, 15, 19, 10, 11, 12, 14, 15, 18, 19, 20, 11, 13, 15, 19, 21

Offset: 0

Author

Rémy Sigrist, Oct 20 2019

Keywords

• nonn
• tabf
• look
• base

Comments

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

- has sum A328566(n),

- has apparently length A002487(n+1),

- has last element n.

Examples

			Table begins:
    0;
    1;
    1, 2;
    3;
    2, 3, 4;
    3, 5;
    3, 5, 6;
    7;
    4, 6, 7, 8;
    5, 7, 9;
    5, 6, 7, 9, 10;
    7, 11;
    6, 7, 10, 11, 12;
    7, 11, 13;
    7, 11, 13, 14;
    ...
		

Links

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

Crossrefs

Cf. A326819 (AND variant), A328568 (XOR variant).

Cf. A002487, A328566.

Programs

Maple

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

PARI

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