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A131218 Gray code/ Silvester-Hadamard binary triangular sequence from 16 X 16 self-similar matrix. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This algorithm gives a real Gray code binary triangular sequence.

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

Clear[c, b, n, a0] 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 A113998 A253084

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

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Last modified June 16 13:37 EDT 2019. Contains 324152 sequences. (Running on oeis4.)