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A152439
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A special case of angular momentum that gives a relatively symmetrical sequence: t(n,m)=4*((2*n - 3)*m*(m - 1)) - 4*(n*(n - 1) - m*(m - 1)).
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0
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0, -2, 1, 2, 0, 0, 0, 0, 0, 12, 5, 0, -3, -4, -3, 0, 40, 22, 8, -2, -8, -10, -8, -2, 8, 90, 57, 30, 9, -6, -15, -18, -15, -6, 9, 30, 168, 116, 72, 36, 8, -12, -24, -28, -24, -12, 8, 36, 72, 280, 205, 140, 85, 40, 5, -20, -35, -40, -35, -20, 5, 40, 85, 140, 432, 330, 240, 162
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The Lande g=s solved so that:
(2*g-3)*J*(J+1)=s*(s+1)-L*(L+1).
Row sums are:
{0, 1, 0, 7, 48, 165, 416, 875, 1632, 2793, 4480,...}
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FORMULA
| t(n,m)=4*((2*n - 3)*m*(m - 1)) - 4*(n*(n - 1) - m*(m - 1)).
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EXAMPLE
| {0},
{-2, 1, 2},
{0, 0, 0, 0, 0},
{12, 5, 0, -3, -4, -3, 0},
{40, 22, 8, -2, -8, -10, -8, -2, 8},
{90, 57, 30, 9, -6, -15, -18, -15, -6, 9, 30},
{168, 116, 72, 36, 8, -12, -24, -28, -24, -12, 8, 36, 72},
{280, 205, 140, 85, 40, 5, -20, -35, -40, -35, -20, 5, 40, 85,140},
{432, 330, 240, 162, 96, 42, 0, -30, -48, -54, -48, -30, 0,42, 96, 162, 240},
{630, 497, 378, 273,182, 105, 42, -7, -42, -63, -70, -63, -42, -7, 42, 105, 182, 273, 378},
{880, 712, 560, 424, 304, 200, 112,40, -16, -56, -80, -88, -80, -56, -16, 40, 112, 200, 304, 424, 560}
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MATHEMATICA
| Clear[t, n, m];
t[n_, m_] = 4*((2*n - 3)*m*(m - 1)) - 4*(n*(n - 1) - m*(m - 1));
Table[Table[t[n, m], {m, -n, n, 1/2}], {n, 0, 5, 1/2}];
Flatten[%]
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CROSSREFS
| Sequence in context: A178473 A164810 A089538 * A070965 A079548 A175620
Adjacent sequences: A152436 A152437 A152438 * A152440 A152441 A152442
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KEYWORD
| tabf,uned,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 04 2008
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