Search: id:A152439
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%I A152439
%S A152439 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,
%T A152439 30,9,6,15,18,15,6,9,30,168,116,72,36,8,12,24,28,24,12,8,36,
%U A152439 72,280,205,140,85,40,5,20,35,40,35,20,5,40,85,140,432,330,240,162
%V A152439 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,
%W A152439 30,9,-6,-15,-18,-15,-6,9,30,168,116,72,36,8,-12,-24,-28,-24,-12,8,36,
%X A152439 72,280,205,140,85,40,5,-20,-35,-40,-35,-20,5,40,85,140,432,330,240,162
%N A152439 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)).
%C A152439 The Lande g=s solved so that:
%C A152439 (2*g-3)*J*(J+1)=s*(s+1)-L*(L+1).
%C A152439 Row sums are:
%C A152439 {0, 1, 0, 7, 48, 165, 416, 875, 1632, 2793, 4480,...}
%F A152439 t(n,m)=4*((2*n - 3)*m*(m - 1)) - 4*(n*(n - 1) - m*(m - 1)).
%e A152439 {0},
%e A152439 {-2, 1, 2},
%e A152439 {0, 0, 0, 0, 0},
%e A152439 {12, 5, 0, -3, -4, -3, 0},
%e A152439 {40, 22, 8, -2, -8, -10, -8, -2, 8},
%e A152439 {90, 57, 30, 9, -6, -15, -18, -15, -6, 9, 30},
%e A152439 {168, 116, 72, 36, 8, -12, -24, -28, -24, -12, 8, 36, 72},
%e A152439 {280, 205, 140, 85, 40, 5, -20, -35, -40, -35, -20, 5, 40, 85,140},
%e A152439 {432, 330, 240, 162, 96, 42, 0, -30, -48, -54, -48, -30, 0,42, 96, 162, 
               240},
%e A152439 {630, 497, 378, 273,182, 105, 42, -7, -42, -63, -70, -63, -42, -7, 42, 
               105, 182, 273, 378},
%e A152439 {880, 712, 560, 424, 304, 200, 112,40, -16, -56, -80, -88, -80, -56, 
               -16, 40, 112, 200, 304, 424, 560}
%t A152439 Clear[t, n, m];
%t A152439 t[n_, m_] = 4*((2*n - 3)*m*(m - 1)) - 4*(n*(n - 1) - m*(m - 1));
%t A152439 Table[Table[t[n, m], {m, -n, n, 1/2}], {n, 0, 5, 1/2}];
%t A152439 Flatten[%]
%Y A152439 Sequence in context: A159767 A164810 A089538 this_sequence A070965 A079548 
               A079071
%Y A152439 Adjacent sequences: A152436 A152437 A152438 this_sequence A152440 A152441 
               A152442
%K A152439 tabf,uned,sign
%O A152439 0,2
%A A152439 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 04 2008

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