|
|
A141418
|
|
Triangle read by rows: T(n,k) = k * (2*n - k - 1) / 2, 1 <= k <= n.
|
|
5
|
|
|
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;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
n-th row = half of Dynkin diagram weights for the Cartan Groups D_n.
n-th row = partial sums of n-th row of A025581. (End)
|
|
REFERENCES
|
R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.
|
|
LINKS
|
|
|
FORMULA
|
T(n, K) = k*(2*n - k - 1)/2.
|
|
EXAMPLE
|
Triangle begins as:
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;
|
|
MAPLE
|
|
|
MATHEMATICA
|
T[n_, k_]= k*(2*n-k-1)/2; Table[T[n, k], {n, 12}, {k, n}]//Flatten
|
|
PROG
|
(Haskell)
a141418 n k = k * (2 * n - k - 1) `div` 2
a141418_row n = a141418_tabl !! (n-1)
a141418_tabl = map (scanl1 (+)) a025581_tabl
(Magma) [k*(2*n-k-1)/2: k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 30 2021
(Sage) flatten([[k*(2*n-k-1)/2 for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Mar 30 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|