

A261349


T(n,k) is the decimal equivalent of a code for k that maximizes the sum of the Hamming distances between (cyclical) adjacent code words; triangle T(n,k), n>=0, 0<=k<=2^n1, read by rows.


1



0, 0, 1, 0, 3, 1, 2, 0, 7, 1, 6, 3, 4, 2, 5, 0, 15, 1, 14, 3, 12, 2, 13, 6, 9, 7, 8, 5, 10, 4, 11, 0, 31, 1, 30, 3, 28, 2, 29, 6, 25, 7, 24, 5, 26, 4, 27, 12, 19, 13, 18, 15, 16, 14, 17, 10, 21, 11, 20, 9, 22, 8, 23, 0, 63, 1, 62, 3, 60, 2, 61, 6, 57, 7, 56, 5
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OFFSET

0,5


COMMENTS

This code might be called "AntiGray code".
The sum of the Hamming distances between (cyclical) adjacent code words of row n gives 0, 2, 6, 20, 56, 144, 352, ... = A014480(n1) for n>1.


LINKS

Alois P. Heinz, Rows n = 0..13, flattened
Wikipedia, Gray code
Wikipedia, Hamming distance


FORMULA

T(n,k) = A003188(k/2) if k even, T(n,k) = 2^n1A003188((k1)/2) else.
A101080(T(n,2k),T(n,2k+1)) = n, A101080(T(n,2k),T(n,2k1)) = n1.
T(n,2^n1) = A083329(n1) for n>0.
T(n,2^n2) = A000079(n2) for n>1.
T(2n,2n) = A003188(n).
T(2n+1,2n+1) = 2*4^n  1  A003188(n) = A083420(n)  A003188(n).


EXAMPLE

Triangle T(n,k) begins:
0;
0, 1;
0, 3, 1, 2;
0, 7, 1, 6, 3, 4, 2, 5;
0, 15, 1, 14, 3, 12, 2, 13, 6, 9, 7, 8, 5, 10, 4, 11;
0, 31, 1, 30, 3, 28, 2, 29, 6, 25, 7, 24, 5, 26, 4, 27, 12, 19, ... ;
0, 63, 1, 62, 3, 60, 2, 61, 6, 57, 7, 56, 5, 58, 4, 59, 12, 51, ... ;


MAPLE

g:= n> Bits[Xor](n, iquo(n, 2)):
T:= (n, k)> (t> `if`(m=0, t, 2^n1t))(g(iquo(k, 2, 'm'))):
seq(seq(T(n, k), k=0..2^n1), n=0..6);


CROSSREFS

Columns k=03 give: A000004, A000225, A000012 (for n>1), A000918 (for n>1).
Row lengths give A000079.
Row sums give A006516.
Cf. A003188, A014480, A083329, A083420, A101080.
Sequence in context: A054869 A201671 A226590 * A227962 A255615 A056931
Adjacent sequences: A261346 A261347 A261348 * A261350 A261351 A261352


KEYWORD

nonn,look,tabf,easy


AUTHOR

Alois P. Heinz, Nov 18 2015


STATUS

approved



