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A141418
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A triangular sequence of coefficients of Dynkin diagram weights for the Cartan Groups D_n: t(n,m)=m*(2*n - m - 1)/2.
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0
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0, 1, 1, 2, 3, 3, 3, 5, 6, 6, 4, 7, 9, 10, 10, 5, 9, 12, 14, 15, 15, 6, 11, 15, 18, 20, 21, 21, 7, 13, 18, 22, 25, 27, 28, 28, 8, 15, 21, 26, 30, 33, 35, 36, 36, 9, 17, 24, 30, 35, 39, 42, 44, 45, 45
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Row sums are:
{0, 2, 8, 20, 40, 70, 112, 168, 240, 330};
Here all the weights are divided by two where they aren't in Cahn.
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REFERENCES
| R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.
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FORMULA
| t(n,m)=m*(2*n - m - 1)/2.
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EXAMPLE
| {0},
{1, 1},
{2, 3, 3},
{3, 5, 6, 6},
{4, 7, 9, 10, 10},
{5, 9, 12, 14, 15, 15},
{6, 11, 15, 18, 20, 21, 21},
{7, 13, 18, 22, 25, 27, 28, 28},
{8, 15, 21, 26, 30, 33, 35, 36, 36},
{9, 17, 24, 30, 35, 39, 42, 44, 45, 45}
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MATHEMATICA
| Clear[T, n, m, a] T[n_, m_] = m*(2*n - m - 1)/2; a = Table[Table[T[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[a]
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CROSSREFS
| Sequence in context: A145281 A151687 A160573 * A130499 A020910 A029065
Adjacent sequences: A141415 A141416 A141417 * A141419 A141420 A141421
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 05 2008
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