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

1, 8, 40, 5, 160, 60, 560, 420, 21, 1792, 2240, 336, 5376, 10080, 3024, 84, 15360, 40320, 20160, 1680, 42240, 147840, 110880, 18480, 330, 112640, 506880, 532224, 147840, 7920, 292864, 1647360, 2306304, 960960, 102960

Offset

3,2

Comments

For a general discussion, please see A213343.

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

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

References

See A213343

Links

Stanislav Sykora, Table of n, a(n) for n = 3..2452

Stanislav Sykora, T(3;N,k) with rows N=3,..,100 and columns k=0,..,floor((N-3)/2)

Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

Formula

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

Example

Some of the 40 triple-quantum transitions for N = 5 and combination index 0: (00000,01011),(10010,11111),...
Starting rows of the triangle T(3;N,k):
  N | k = 0, 1, ..., floor((N-3)/2)
  3 |   1
  4 |   8
  5 |  40   5
  6 | 160  60
  7 | 560 420 21

Mathematica

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 *)

Prog

(PARI) See A213343; set thisq = 3.

Crossrefs

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

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

Sequence in context: A319362 A154425 A120931 * A207360 A226904 A305075

Adjacent sequences: A213342 A213343 A213344 * A213346 A213347 A213348

Keyword

tabf,nonn

Author

Stanislav Sykora, Jun 12 2012

Status

approved