|
Search: id:A141419
|
|
|
| A141419 |
|
A triangular sequence of coefficients of Dynkin diagram weights for the Cartan Groups B_n: t(n,m)=m*(2*n - m + 1)/2. |
|
+0
1
|
|
| 1, 2, 3, 3, 5, 6, 4, 7, 9, 10, 5, 9, 12, 14, 15, 6, 11, 15, 18, 20, 21, 7, 13, 18, 22, 25, 27, 28, 8, 15, 21, 26, 30, 33, 35, 36, 9, 17, 24, 30, 35, 39, 42, 44, 45, 10, 19, 27, 34, 40, 45, 49, 52, 54, 55
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Row sums are:
{1, 5, 14, 30, 55, 91, 140, 204, 285, 385};
Here all the weights are divided by two where they aren't in Cahn.
|
|
REFERENCES
|
R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.
|
|
FORMULA
|
t(n,m)=m*(2*n - m + 1)/2.
|
|
EXAMPLE
|
{1},
{2, 3},
{3, 5, 6},
{4, 7, 9, 10},
{5, 9, 12, 14, 15},
{6, 11, 15, 18, 20, 21},
{7, 13, 18, 22, 25, 27, 28},
{8, 15, 21, 26, 30, 33, 35, 36},
{9, 17, 24, 30, 35, 39, 42, 44, 45},
{10, 19, 27, 34, 40, 45, 49, 52, 54, 55}
|
|
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]
|
|
CROSSREFS
|
Sequence in context: A085312 A046530 A003558 this_sequence A072451 A023156 A051599
Adjacent sequences: A141416 A141417 A141418 this_sequence A141420 A141421 A141422
|
|
KEYWORD
|
nonn,uned,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 05 2008
|
|
|
Search completed in 0.002 seconds
|
