A131218 Gray code/ Silvester-Hadamard binary triangular sequence from 16 X 16 self-similar matrix.

1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1

Offset

1,1

Comments

See A140820 for another version.

Links

Table of n, a(n) for n=1..105.

Formula

a(n,m) = Antidiagonal[HadamardMatrix[n,m]]

Example

{1},
{1, 1},
{1, 0, 1},
{1, 0, 0, 1},
{1, 1, 0, 1, 1},
{1, 1, 0, 0, 1, 1},
{1, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 1},
{1, 1, 0, 0, 0, 0, 0, 1, 1},
{1, 1, 1, 1, 0, 0, 1, 1, 1, 1},
{1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1},
{1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1},
{1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1},
{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}

Mathematica

c[i_, k_]:=Floor[Mod[i/2^k, 2]];
b[i_, k_]=If[c[i, k]==0&&c[i, k+1]\[Equal]0, 0, If[c[ i, k]==1&&c[i, k+1]\[Equal]1, 0, 1]];
a0=Table[If[Sum[b[i, k]*b[j, k], {k, 0, n}]\[Equal]0, 1, 0], {j, 0, n}, {i, 0, n}];
ListDensityPlot[a0, Mesh\[Rule]False];
c=Delete[Table[Reverse[Table[a0[[n, l-n]], {n, 1, l-1}]], {l, 1, Dimensions[a0][[1]]+1}], 1];
Flatten[c]

Crossrefs

Cf. A121801, A122944, A123949, A140820.

Sequence in context: A154957 A140865 A114000 * A174391 A343910 A329682

Adjacent sequences: A131215 A131216 A131217 * A131219 A131220 A131221

Keyword

nonn,uned,tabl,obsc

Author

Roger L. Bagula, Sep 27 2007

Extensions

This looks interesting, but I do not understand the definition. - N. J. A. Sloane, Oct 16 2008

Status

approved