|
| |
|
|
A152420
|
|
A triangular sequence related to angular momentum: t(n,m)=4*(n*(n-1)-m*(m-1)).
|
|
0
| |
|
|
0, -4, -1, 0, -8, -3, 0, 1, 0, -12, -5, 0, 3, 4, 3, 0, -16, -7, 0, 5, 8, 9, 8, 5, 0, -20, -9, 0, 7, 12, 15, 16, 15, 12, 7, 0, -24, -11, 0, 9, 16, 21, 24, 25, 24, 21, 16, 9, 0, -28, -13, 0, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11, 0, -32, -15, 0, 13, 24, 33, 40, 45, 48, 49, 48, 45
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| The Lande splitting factor or g-factor is:
g=1+(j*(j+1)+s(s+1)-L*(L+1))/2*j*(j+1);
The term:
s(s+1)-L*(L+1))
is the one this sequence look at.
The row sums are:
{0, -5, -10, -7, 12, 55, 130, 245, 408, 627, 910,...}
|
|
|
FORMULA
| t(n,m)=4*(n*(n-1)-m*(m-1)).
|
|
|
EXAMPLE
| {0},
{-4, -1, 0},
{-8, -3, 0, 1, 0},
{-12, -5, 0, 3, 4, 3, 0},
{-16, -7, 0, 5, 8, 9, 8, 5, 0},
{-20, -9, 0, 7, 12, 15, 16, 15, 12, 7, 0},
{-24, -11, 0, 9, 16, 21, 24, 25, 24, 21, 16, 9, 0},
{-28, -13, 0, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11, 0},
{-32, -15, 0, 13, 24, 33, 40, 45, 48, 49, 48, 45, 40, 33, 24, 13, 0},
{-36, -17, 0, 15, 28, 39, 48, 55, 60, 63, 64, 63, 60, 55, 48, 39, 28, 15, 0},
{-40, -19, 0, 17, 32, 45, 56, 65, 72, 77, 80, 81, 80, 77, 72, 65, 56, 45, 32, 17, 0}
|
|
|
MATHEMATICA
| Clear[t, n, m];
t[n_, m_] = 4*(n*(n - 1) - m*(m - 1));
Table[Table[t[n, m], {m, -n, n, 1/2}], {n, 0, 5, 1/2}]
Flatten[%]
|
|
|
CROSSREFS
| Sequence in context: A062175 A085659 A176219 * A050465 A134575 A095831
Adjacent sequences: A152417 A152418 A152419 * A152421 A152422 A152423
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Dec 03 2008
|
| |
|
|
