A348684 Triangle read by rows, T(n, k) = 2*n - HammingWeight(k), for 0 <= k <= n.

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

Offset: 0

Author

Peter Luschny, Oct 29 2021

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0]  0;
[1]  2,  1;
[2]  4,  3,  3;
[3]  6,  5,  5,  4;
[4]  8,  7,  7,  6,  7;
[5] 10,  9,  9,  8,  9,  8;
[6] 12, 11, 11, 10, 11, 10, 10;
[7] 14, 13, 13, 12, 13, 12, 12, 11;
[8] 16, 15, 15, 14, 15, 14, 14, 13, 15;
[9] 18, 17, 17, 16, 17, 16, 16, 15, 17, 16;
		

Crossrefs

Cf. A000120, A005843, A005187, A057427 (row gcd).

Cf. A348685, A348687, A348676.

Programs

Maple

HammingWeight := n -> add(i, i = convert(n, base, 2)):
A348684 := (n, k) -> 2*n - HammingWeight(k):
seq(seq(A348684(n, k), k = 0..n), n = 0..10);

Mathematica

Table[2*n - DigitCount[k, 2, 1], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Oct 30 2021 *)