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

%I

%S 1,8,40,5,160,60,560,420,21,1792,2240,336,5376,10080,3024,84,15360,

%T 40320,20160,1680,42240,147840,110880,18480,330,112640,506880,532224,

%U 147840,7920,292864,1647360,2306304,960960,102960

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

%C For a general discussion, please see A213343.

%C This a(n) is for triple-quantum transitions (q = 3).

%C It lists the flattened triangle T(3;N,k) with rows N = 3,5,... and columns k = 0..floor((N-3)/2).

%D See A213343

%H Stanislav Sykora, <a href="/A213345/b213345.txt">Table of n, a(n) for n = 3..2452</a>

%H 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>

%F Set q = 3 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

%e Some of the 40 triple-quantum transitions for N = 5 and combination index 0: (00000,01011),(10010,11111),...

%e Starting rows of the triangle T(3;N,k):

%e N | k = 0, 1, ..., floor((N-3)/2)

%e 3 | 1

%e 4 | 8

%e 5 | 40 5

%e 6 | 160 60

%e 7 | 560 420 21

%o (PARI) See A213343; set thisq = 3.

%Y Cf. A051288 (q=0), A213343 (q=1), A213344 (q=2), A213346 to A213352 (q=4..10).

%Y Cf. A001789 (first column), A002696 (row sums).

%K tabf,nonn

%O 3,2

%A _Stanislav Sykora_, Jun 12 2012

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Last modified January 22 12:13 EST 2019. Contains 319363 sequences. (Running on oeis4.)