A348685 Triangle read by rows, T(n, k) = 2^(2*n - HammingWeight(k)), for 0 <= k <= n.

1, 4, 2, 16, 8, 8, 64, 32, 32, 16, 256, 128, 128, 64, 128, 1024, 512, 512, 256, 512, 256, 4096, 2048, 2048, 1024, 2048, 1024, 1024, 16384, 8192, 8192, 4096, 8192, 4096, 4096, 2048, 65536, 32768, 32768, 16384, 32768, 16384, 16384, 8192, 32768

Offset: 0

Author

Peter Luschny, Oct 29 2021

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1;
[1] 4,      2;
[2] 16,     8,      8;
[3] 64,     32,     32,     16;
[4] 256,    128,    128,    64,    128;
[5] 1024,   512,    512,    256,   512,    256;
[6] 4096,   2048,   2048,   1024,  2048,   1024,  1024;
[7] 16384,  8192,   8192,   4096,  8192,   4096,  4096,  2048;
[8] 65536,  32768,  32768,  16384, 32768,  16384, 16384, 8192,  32768;
[9] 262144, 131072, 131072, 65536, 131072, 65536, 65536, 32768, 131072, 65536;
		

Crossrefs

Cf. A000120, A000079, A000302, A046161.

Cf. A348684, A348687, A348676.

Programs

Maple

HammingWeight := n -> add(i, i = convert(n, base, 2)):
A348685 := (n, k) -> 2^(2*n - HammingWeight(k)):
seq(seq(A348685(n, k), k = 0..n), n = 0..8);

Mathematica

Table[2^(2*n - DigitCount[k, 2, 1]), {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, Oct 30 2021 *)