A348685 - OEIS

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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..44.

EXAMPLE

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;

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 *)

CROSSREFS

Cf. A000120, A000079, A000302, A046161.

Cf. A348684, A348687, A348676.

Sequence in context: A302213 A090881 A191452 * A110485 A240988 A154383

Adjacent sequences: A348682 A348683 A348684 * A348686 A348687 A348688

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Oct 29 2021

STATUS

approved