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Search: id:A131218
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| A131218 |
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Gray code/ Silvester-Hadamard binary triangular sequence from 16 X 16 self-similar matrix. |
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+0
3
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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This algorithm gives a real Gray code binary triangular sequence.
See A140820 for another version.
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FORMULA
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a(n,m) = Antidiagonal[HadamardMatrix[n,m]]
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EXAMPLE
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{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}
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A121801, A122944, A123949, A140820.
Sequence in context: A127970 A140865 A114000 this_sequence A113998 A070909 A115954
Adjacent sequences: A131215 A131216 A131217 this_sequence A131219 A131220 A131221
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KEYWORD
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nonn,uned,tabl,obsc
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 27 2007
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EXTENSIONS
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This looks interesting, but I do not understand the definition. - njas, Oct 16 2008
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