A348676 Triangle read by rows, T(n, k) = 2^(n - HammingWeight(k)), for 0 <= k <= n.

1, 2, 1, 4, 2, 2, 8, 4, 4, 2, 16, 8, 8, 4, 8, 32, 16, 16, 8, 16, 8, 64, 32, 32, 16, 32, 16, 16, 128, 64, 64, 32, 64, 32, 32, 16, 256, 128, 128, 64, 128, 64, 64, 32, 128, 512, 256, 256, 128, 256, 128, 128, 64, 256, 128, 1024, 512, 512, 256, 512, 256, 256, 128, 512, 256, 256

Offset: 0

Author

Peter Luschny, Oct 29 2021

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1;
[1] 2,   1;
[2] 4,   2,   2;
[3] 8,   4,   4,   2;
[4] 16,  8,   8,   4,   8;
[5] 32,  16,  16,  8,   16,  8;
[6] 64,  32,  32,  16,  32,  16,  16;
[7] 128, 64,  64,  32,  64,  32,  32,  16;
[8] 256, 128, 128, 64,  128, 64,  64,  32, 128;
[9] 512, 256, 256, 128, 256, 128, 128, 64, 256, 128;
		

Crossrefs

Cf. A000120, A000079, A060818, A054243 (row gcd).

Cf. A348684, A348685, A348687.

Programs

Maple

HammingWeight := n -> add(i, i = convert(n, base, 2)):
A348676 := (n, k) -> 2^(n - HammingWeight(k)):
seq(seq(A348676(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 *)