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A140820
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Triangle read by rows: let c(i,k)=Floor[Mod[i/2^k, 2]]; b(i,k)=If[c[i, k] == 0 && c[i, k + 1] == 0, 0, If[c[ i, k] == 1 && c[i, k + 1] ==1, 0, 1]]; then t(i,j)=If[Sum[b[i, k]*b[j, k], {k, 0, n}] == 0, 1, 0].
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1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are: {1, 1, 1, 2, 2, 1, 2, 4, 4, 2, 1, 2, 4, 2, 4, 8, 8, ...}.
In this method the information is complete: as it is a symbol representation instead of {0,1}, {-1,1} or {1,2} can be used in the output just as well.
This kind of code is used in minimal coding representations like the binary Gray code.
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FORMULA
| c(i,k)=Floor[Mod[i/2^k, 2]]; b(i,k)=If[c[i, k] == 0 && c[i, k + 1] == 0, 0, If[c[ i, k] == 1 && c[i, k + 1] ==1, 0, 1]]; t(i,j)=If[Sum[b[i, k]*b[j, k], {k, 0, n}] == 0, 1, 0].
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EXAMPLE
| {1},
{1, 0},
{1, 0, 0},
{1, 1, 0, 0},
{1, 1, 0, 0, 0},
{1, 0, 0, 0, 0, 0},
{1, 0, 0, 1, 0, 0, 0},
{1, 1, 1, 1, 0, 0, 0, 0},
{1, 1, 1, 1, 0, 0, 0, 0, 0},
{1, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}
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MATHEMATICA
| Clear[c, b, n, a0, d] c[i_, k_] := Floor[Mod[i/2^k, 2]]; b[i_, k_] = If[c[i, k] == 0 && c[i, k + 1] == 0, 0, If[c[ i, k] == 1 && c[i, k + 1] == 1, 0, 1]]; n = 16; a0 = Table[Table[If[Sum[b[i, k]*b[j, k], {k, 0, n}] == 0, 1, 0], {j, 0, i}], {i, 0, n}]; Flatten[a0]
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CROSSREFS
| Cf. A131218.
Sequence in context: A176918 A176890 A164057 * A167501 A185175 A147612
Adjacent sequences: A140817 A140818 A140819 * A140821 A140822 A140823
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 17 2008
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