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A213345 3-quantum transitions in systems of N>=3 spin 1/2 particles, in columns by combination indices.

%I A213345 #24 Nov 18 2019 22:06:53
%S A213345 1,8,40,5,160,60,560,420,21,1792,2240,336,5376,10080,3024,84,15360,
%T A213345 40320,20160,1680,42240,147840,110880,18480,330,112640,506880,532224,
%U A213345 147840,7920,292864,1647360,2306304,960960,102960
%N A213345 3-quantum transitions in systems of N>=3 spin 1/2 particles, in columns by combination indices.
%C A213345 For a general discussion, please see A213343.
%C A213345 This a(n) is for triple-quantum transitions (q = 3).
%C A213345 It lists the flattened triangle T(3;N,k) with rows N = 3,5,... and columns k = 0..floor((N-3)/2).
%D A213345 See A213343
%H A213345 Stanislav Sykora, <a href="/A213345/b213345.txt">Table of n, a(n) for n = 3..2452</a>
%H A213345 Stanislav Sykora, <a href="/A213345/a213345.txt">T(3;N,k) with rows N=3,..,100 and columns k=0,..,floor((N-3)/2)</a>
%H A213345 Stanislav Sýkora, <a href="http://www.ebyte.it/stan/blog12to14.html#14Dec31">Magnetic Resonance on OEIS</a>, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
%F A213345 Set q = 3 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
%e A213345 Some of the 40 triple-quantum transitions for N = 5 and combination index 0: (00000,01011),(10010,11111),...
%e A213345 Starting rows of the triangle T(3;N,k):
%e A213345   N | k = 0, 1, ..., floor((N-3)/2)
%e A213345   3 |   1
%e A213345   4 |   8
%e A213345   5 |  40   5
%e A213345   6 | 160  60
%e A213345   7 | 560 420 21
%t A213345 With[{q = 3}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 13}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* _Michael De Vlieger_, Nov 18 2019 *)
%o A213345 (PARI) See A213343; set thisq = 3.
%Y A213345 Cf. A051288 (q=0), A213343 (q=1), A213344 (q=2), A213346 to A213352 (q=4..10).
%Y A213345 Cf. A001789 (first column), A002696 (row sums).
%K A213345 tabf,nonn
%O A213345 3,2
%A A213345 _Stanislav Sykora_, Jun 12 2012