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%I #10 Oct 30 2021 06:03:15
%S 1,4,2,16,8,8,64,32,32,16,256,128,128,64,128,1024,512,512,256,512,256,
%T 4096,2048,2048,1024,2048,1024,1024,16384,8192,8192,4096,8192,4096,
%U 4096,2048,65536,32768,32768,16384,32768,16384,16384,8192,32768
%N Triangle read by rows, T(n, k) = 2^(2*n - HammingWeight(k)), for 0 <= k <= n.
%e Triangle starts:
%e [0] 1;
%e [1] 4, 2;
%e [2] 16, 8, 8;
%e [3] 64, 32, 32, 16;
%e [4] 256, 128, 128, 64, 128;
%e [5] 1024, 512, 512, 256, 512, 256;
%e [6] 4096, 2048, 2048, 1024, 2048, 1024, 1024;
%e [7] 16384, 8192, 8192, 4096, 8192, 4096, 4096, 2048;
%e [8] 65536, 32768, 32768, 16384, 32768, 16384, 16384, 8192, 32768;
%e [9] 262144, 131072, 131072, 65536, 131072, 65536, 65536, 32768, 131072, 65536;
%p HammingWeight := n -> add(i, i = convert(n, base, 2)):
%p A348685 := (n, k) -> 2^(2*n - HammingWeight(k)):
%p seq(seq(A348685(n, k), k = 0..n), n = 0..8);
%t Table[2^(2*n - DigitCount[k, 2, 1]), {n, 0, 8}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Oct 30 2021 *)
%Y Cf. A000120, A000079, A000302, A046161.
%Y Cf. A348684, A348687, A348676.
%K nonn,tabl
%O 0,2
%A _Peter Luschny_, Oct 29 2021
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