A348676
Triangle read by rows, T(n, k) = 2^(n - HammingWeight(k)), for 0 <= k <= n.
Original entry on oeis.org
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
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;
-
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);
-
Table[2^(n - DigitCount[k, 2, 1]), {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Oct 30 2021 *)
A348684
Triangle read by rows, T(n, k) = 2*n - HammingWeight(k), for 0 <= k <= n.
Original entry on oeis.org
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
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;
-
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);
-
Table[2*n - DigitCount[k, 2, 1], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Oct 30 2021 *)
A348685
Triangle read by rows, T(n, k) = 2^(2*n - HammingWeight(k)), for 0 <= k <= n.
Original entry on oeis.org
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
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;
-
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);
-
Table[2^(2*n - DigitCount[k, 2, 1]), {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, Oct 30 2021 *)
Showing 1-3 of 3 results.