%I #10 Oct 30 2021 06:03:11

%S 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,

%T 128,64,64,32,64,32,32,16,256,128,128,64,128,64,64,32,128,512,256,256,

%U 128,256,128,128,64,256,128,1024,512,512,256,512,256,256,128,512,256,256

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

%e Triangle starts:

%e [0] 1;

%e [1] 2, 1;

%e [2] 4, 2, 2;

%e [3] 8, 4, 4, 2;

%e [4] 16, 8, 8, 4, 8;

%e [5] 32, 16, 16, 8, 16, 8;

%e [6] 64, 32, 32, 16, 32, 16, 16;

%e [7] 128, 64, 64, 32, 64, 32, 32, 16;

%e [8] 256, 128, 128, 64, 128, 64, 64, 32, 128;

%e [9] 512, 256, 256, 128, 256, 128, 128, 64, 256, 128;

%p HammingWeight := n -> add(i, i = convert(n, base, 2)):

%p A348676 := (n, k) -> 2^(n - HammingWeight(k)):

%p seq(seq(A348676(n, k), k = 0..n), n = 0..10);

%t Table[2^(n - DigitCount[k, 2, 1]), {n, 0, 10}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Oct 30 2021 *)

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

%Y Cf. A348684, A348685, A348687.

%K nonn,tabl

%O 0,2

%A _Peter Luschny_, Oct 29 2021