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A142354
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A triangular sequence "representation" of the modulo 10 Integer field: t(+)(n,m)=Mod[n + m, 10]; t(x)(n,m)=Mod[n*m, 10]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),10].
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0
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0, 0, 2, 0, 6, 6, 0, 2, 0, 4, 0, 0, 8, 4, 8, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 0, 2, 0, 6, 6, 0, 8, 0, 6, 6, 0, 2, 0, 4, 4, 0, 2, 0, 4, 0, 0, 8, 4, 8, 0, 0, 8, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums are:
{0, 2, 12, 6, 20, 0, 12, 32, 16, 40, 0}.
Modulo ten they are:
{0, 2, 2, 6, 0, 0, 2, 2, 6, 0, 0}.
The block:
{0},
{0, 2},
{0, 6, 6},
{0, 2, 0, 4},
{0, 0, 8, 4, 8},
{0, 0, 0, 0, 0, 0},
shows up in three places.
Only even {0,2,4,6,8} show up.
It may be a field representation, but can you get the
original tables back from it?
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FORMULA
| t(+)(n,m)=Mod[n + m, 10]; t(x)(n,m)=Mod[n*m, 10]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),10].
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EXAMPLE
| {0},
{0, 2},
{0, 6, 6},
{0, 2, 0, 4},
{0, 0, 8, 4, 8},
{0, 0, 0, 0, 0, 0},
{0, 2, 6, 2, 0, 0, 2},
{0, 6, 6, 0, 8, 0, 6, 6},
{0, 2, 0, 4, 4, 0, 2, 0, 4},
{0, 0, 8, 4, 8, 0, 0, 8, 4, 8},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
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MATHEMATICA
| Clear[t1, t2, t, n, m, a]; t1[n_, m_] = Mod[n + m, 10]; t2[n_, m_] = Mod[n*m, 10]; t[n_, m_] = Mod[t1[n, m]*t2[n, m], 10]; a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]
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CROSSREFS
| Sequence in context: A140247 A111520 A145419 * A105110 A064696 A021488
Adjacent sequences: A142351 A142352 A142353 * A142355 A142356 A142357
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 19 2008
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